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| 1 | THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS显示文摘The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators. | Lu Shanzhen and Yang Dachun (Beijing Normal University, China) | 1995 | Analysis in Theory and Applications1995，11，3： | 49 |
| 2 | Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces显示文摘Let(X,d,μ)be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of Hyto¨nen.We prove that the L p(μ)-boundedness with p∈(1,∞)of the Marcinkiewicz integral is equivalent to either of its boundedness from L1(μ)into L1,∞(μ)or from the atomic Hardy space H1(μ)into L1(μ).Moreover,we show that,if the Marcinkiewicz integral is bounded from H1(μ)into L1(μ),then it is also bounded from L∞(μ)into the space RBLO(μ)(the regularized BLO),which is a proper subset of RBMO(μ)(the regularized BMO)and,conversely,if the Marcinkiewicz integral is bounded from L∞b(μ)(the set of all L∞(μ)functions with bounded support)into the space RBMO(μ),then it is also bounded from the finite atomic Hardy space H1,∞fin(μ)into L1(μ).These results essentially improve the known results even for non-doubling measures. | LIN HaiBo YANG DaChun | 2014 | Science China Mathematics2014，57，1： | 25 |
| 3 | Interpolation of Morrey-Campanato and related smoothness spaces显示文摘We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property. | YUAN Wen SICKEL Winfried YANG DaChun | 2015 | Science China Mathematics2015，58，9： | 19 |
| 4 | TRPV1 activation improves exercise endurance and energy metabolism through PGC-1α upregulation in mice显示文摘 | Zhidan Luo Liqun Ma Zhigang Zhao Hongbo He Dachun Yang Xiaoli Feng Shuangtao Ma Xiaoping Chen Tianqi Zhu Tingbing Cao Daoyan Liu Bernd Nilius Yu Huang Zhencheng Yan Zhiming Zhu | 2012 | Cell Research2012，22，3： | 18 |
| 5 | Anisotropic Hardy-Lorentz spaces and their applications显示文摘Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on Rn.As applications, we first prove that Hp,q A(Rn) is an intermediate space between H^(p1,q1)_A(Rn) and H^(p2,q2)_A(R^n) with 0 < p1 < p < p2 < ∞ and q1, q, q2 ∈(0, ∞], and also between H^(p,q1)_A(Rn) and H^(p,q2)_A(R^n) with p ∈(0, ∞)and 0 < q1 < q < q2 ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H^(p,q)_A(R^n) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calder′on-Zygmund operators from H^(p,∞)_A(R^n) to the weak Lebesgue space L^(p,∞)(R^n)(or to H^p_A(R^n)) in the ln λcritical case, from H^(p,q)_A(R^n) to L^(p,q)(R^n)(or to H^(p,q)_A(R^n)) with δ∈(0,(lnλ)/(ln b)], p ∈(1/(1+,δ),1] and q ∈(0, ∞], as well as the boundedness of some Calderon-Zygmund operators from H^(p,q)_A(R^n) to L^(p,∞)(R^n), where b := | det A|,λ_:= min{|λ| : λ∈σ(A)} and σ(A) denotes the set of all eigenvalues of A. | LIU Jun YANG DaChun YUAN Wen | 2016 | Science China Mathematics2016，59，9： | 13 |
| 6 | Local Hardy spaces of Musielak-Orlicz type and their applications显示文摘Letφ:R n × [0,∞) → [0,∞) be a function such that φ(x,·) is an Orlicz function and (·,t) ∈ A ∞loc (Rn) (the class of local weights introduced by Rychkov).In this paper,the authors introduce a local Musielak-Orlicz Hardy space hφ(Rn) by the local grand maximal function,and a local BMO-type space bmoφ(Rn) which is further proved to be the dual space of hφ(Rn).As an application,the authors prove that the class of pointwise multipliers for the local BMO-type space bmo φ (Rn),characterized by Nakai and Yabuta,is just the dual of L 1 (Rn) + h Φ 0 (Rn),where φ is an increasing function on (0,∞) satisfying some additional growth conditions and Φ 0 a Musielak-Orlicz function induced by φ.Characterizations of hφ(Rn),including the atoms,the local vertical and the local nontangential maximal functions,are presented.Using the atomic characterization,the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of hφ(Rn),from which,the authors further deduce some criterions for the boundedness on hφ(Rn) of some sublinear operators.Finally,the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on hφ(Rn). | YANG DaChun YANG SiBei | 2012 | Science China Mathematics2012，55，8： | 13 |
| 7 | Applications of Orlicz-Hardy spaces associated with operators satisfying Poisson estimates显示文摘Let L be a linear operator in L2 (Rn) and generate an analytic semigroup {e-tL } t 0 with kernel satisfying an upper bound estimate of Poisson type,whose decay is measured by θ(L) ∈ (0,∞).Let Φ be a positive,continuous and strictly increasing function on (0,∞),which is of strictly critical lower type p Φ∈ (n/(n + θ(L)),1].Denote by H Φ,L (Rn) the Orlicz-Hardy space introduced in Jiang,Yang and Zhou's paper in 2009.If Φ is additionally of upper type 1 and subadditive,the authors then show that the Littlewood-Paley g-function g L maps H Φ,L (Rn) continuously into L Φ (Rn) and,moreover,the authors characterize H Φ,L (Rn) in terms of the Littlewood-Paley g λ-function with λ∈ (n(2/p Φ + 1),∞).If Φ is further slightly strengthened to be concave,the authors show that a generalized Riesz transform associated with L is bounded from H Φ,L (Rn) to the Orlicz space L Φ (Rn) or the Orlicz-Hardy space H Φ (Rn);moreover,the authors establish a new subtle molecular characterization of H Φ,L (Rn) associated with L and,as applications,the authors then show that the corresponding fractional integral L-γ for certain γ∈ (0,∞) maps H Φ,L (Rn) continuously into H Φ,L (Rn),where Φ satisfies the same properties as Φ and is determined by Φ and γ,and also that L has a bounded holomorphic functional calculus in H Φ,L (Rn).All these results are new even when Φ(t) ≡ tp for all t ∈ (0,∞) and p ∈ (n/(n + θ(L)),1]. | LIANG YiYu YANG DaChun YANG SiBei | 2011 | Science China Mathematics2011，54，11： | 11 |
| 8 | BOUNDEDNESS OF VECTOR-VALUED OPERATORS ON WEIGHTED HERZ SPACES显示文摘In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue o f the Hardy-Littlewood maximal operator; and using this,the authors obtain the weighted inequalies for a wide class of sublinear singular operators defined on Rn which include the Calderon-Zygmund operators as special cases. The fractional versions of these results are also given. | Tang Lin Yang Dachun | 2000 | Analysis in Theory and Applications2000，16，2： | 11 |
| 9 | Orlicz-Hardy spaces associated with operators显示文摘Let L be a linear operator in L2(Rn) and generate an analytic semigroup {e-tL}t 0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0, ∞) be of upper type 1 and of critical lower type p0(ω) ∈ (n/(n + θ(L)), 1] and ρ(t) = t-1/ω-1(t-1) for t ∈ (0, ∞). We introduce the Orlicz-Hardy space Hω, L(Rn) and the BMO-type space BMOρ, L(Rn) and establish the John-Nirenberg inequality for BMOρ, L(Rn) functions and the duality relation between Hω, L(Rn) and BMOρ, L*(Rn), where L* denotes the adjoint operator of L in L2(Rn). Using this duality relation, we further obtain the ρ-Carleson measure characterization of BMOρ, L*(Rn) and the molecular characterization of Hω, L(Rn); the latter is used to establish the boundedness of the generalized fractional operator Lρ- γfrom Hω, L(Rn) to HL1(Rn) or Lq(Rn) with certain q > 1, where HL1(Rn) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking ω(t) = tp for t ∈ (0, ∞) and p ∈ (n/(n + θ(L)), 1]. | JIANG RenJin YANG DaChun ZHOU Yuan | 2009 | Science China Mathematics2009，52，5： | 10 |
| 10 | Some Characterizations of Weighted Herz-type Hardy Spaces and Their Applications | Lu Shanzhen (Department of Mathematics,Beijing Normal University,Beijing,100875,China)(E-mail:lusz@bnu.edu.cn)Yang Dachun (Department of Mathematics,Beijing Normal University,Beijin9,100875,China)(E-mail:dcyang@bnu.edu.cn) | 1997 | Acta Mathematica Sinica,English Series1997，13，1： | 10 |
| 11 | Boundedness of Marcinkiewicz integrals and their commutators in H^1(R^n×R^m)显示文摘The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn × Rm) to the Lebesgue space L1(Rn × Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn × Rm) to the Lebesgue space Lq(Rn × Rm) for some q>1. | YANG Dachun ZHOU Yuan | 2006 | Science China Mathematics2006，49，6： | 6 |
| 12 | INHOMOGENEOUS BESOV AND TRIEBEL-LIZORKING SPACES ON SPACES OF HOMOGENEOUS TYPE显示文摘The authors introduce the inhomogeneous esov space and the inhomogeneous Triebel-Lizorkin space on spaces of homogeneous type; and present their atom and molecule decompositions, their dual spaces and the complex interpolation theorems. They also establishe the relation between the homogoeneous Besov space and the inhomogeneous one, and between the homogeneous Triebel-Lizorkin space and the inhomogeneous one. Moreover,they establish T1 theorems for these inhomogeneous spaces when a≠0, and applythese T1 theorems to give new characterizations of these | Yongsheng Han (1) Shanzhen Lu (2) Dachun Yang (2) | 1999 | Analysis in Theory and Applications1999，15，3： | 6 |
| 13 | Real-variable characterizations of anisotropic product Musielak-Orlicz Hardy spaces显示文摘Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces. | FAN XingYa HE JianXun LI BaoDe YANG DaChun | 2017 | Science China Mathematics2017，60，11： | 5 |
| 14 | Down-regulation of microRNA-26b modulates non-small cell lung cancer cells chemoresistance and migration through the association of PTEN显示文摘在非小的房间肺癌症(NSCLC ) 探索 microRNA-26b (miR-26b ) 的效果房间,我们由量的反向的 transcriptase 聚合酶链反应与 NSCLC 从人的病人在 4 根 NSCLC 房间线和 10 件临床的样品调查了 miR-26b 的 mRNA 层次。miR-26b 在 NSCLC 房间和人的癌纸巾是显著地下面调整的,这被发现。合成 oligonucleotides 在 NSCLC 房间线 H1299 和 A549 房间习惯于起来调整或下面调整 miR-26b。结果证明下面调整、起来调整的 miR-26b 没在 H1299 或 A549 房间在癌症房间增长上有效果,而 miR-26b 在表示上增加了癌症房间移植并且减少了 cisplatin chemosensitivity。磷酸酶和 tensin 相当或相同的事物(PTEN ) 被证实由由双酶的记者试金的 miR-26b 直接固定,并且在 miR-26b 是下面调整的过去表示的 NSCLC 房间。最后,当 PTEN 在 NSCLC 房间是起来调整的时,它在 NSCLC 移植和 cisplatin chemosensitivity 上颠倒了 miR-2b 在表示上的效果。在结论,我们的数据在调整 NSCLC 显示出 miR-26b 的功能的机制。它显示 miR-26b 可以通过 PTEN 的规定调整 NSCLC 移植和 chemosensitivity。 | Naixin Liang Xiaoyun Zhou Ming Zhao Dachun Zhao Zhaohui Zhu Shanqing Li Huaxia Yang | 2015 | Acta Biochimica et Biophysica Sinica2015，47，7： | 4 |
| 15 | Weak Hardy-type spaces associated with ball quasi-Banach function spaces I:Decompositions with applications to boundedness of Calderón-Zygmund operators显示文摘Let X be a ball quasi-Banach function space on R^(n).In this article,we introduce the weak Hardytype space WH_(X)(R^(n)),associated with X,via the radial maximal function.Assuming that the powered HardyLittlewood maximal operator satisfies some Fefferman-Stein vector-valued maximal inequality on X as well as it is bounded on both the weak ball quasi-Banach function space WX and the associated space,we then establish several real-variable characterizations of WH_(X)(R^(n)),respectively,in terms of various maximal functions,atoms and molecules.As an application,we obtain the boundedness of Calderón-Zygmund operators from the Hardy space H_(X)(R^(n))to WH_(X)(Rn),which includes the critical case.All these results are of wide applications.Particularly,when X:=M^(q)_(p)(R^(n))(the Morrey space),X:=L^(p)(R^(n))(the mixed-norm Lebesgue space)and X:=(EΦq)t(Rn)(the Orlicz-slice space),which are all ball quasi-Banach function spaces rather than quasiBanach function spaces,all these results are even new.Due to the generality,more applications of these results are predictable. | Yangyang Zhang Dachun Yang Wen Yuan Songbai Wang | 2021 | Science China Mathematics2021，64，9： | 3 |
| 16 | THE CENTRAL CAMPANATO SPACES AND ITS APPLICATION显示文摘Let 1<p<∞,α≥0 and K be a local field.In this paper,the author introduces the spaces J_p^a(K)and the central Campanato spaces C)_a,p(K)as well as the S_p,a-and S_p,a^+-type singular integrals.Then,the author investigates the behavior of these singular integrals and their altered operators on these spaces. | Yang Dachun (Beijing Normal University,China) | 1994 | Analysis in Theory and Applications1994，10，4： | 3 |
| 17 | Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces显示文摘Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range. | Xianjie YAN Dachun YANG Wen YUAN | 2020 | Frontiers of Mathematics in China2020，15，4： | 3 |
| 18 | Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces显示文摘在内在的措施是仅仅满足一些生长状况的非否定的 Radonmeasure 的假设下面,作者与包括 Calderon-Zygmundoperators 和 Lipschitz 功能作为例子产生的整流器的 Lipschitz 功能为整流器的一个班证明那,他们在 Lebesgue 空格或 Hardyspace H^1 的围住的海角(μ)等价于他们满足的一些端点估计。甚至当内在的措施μ是 d 维的 Lebesgue 措施时,这结果是新的。 | Xiaoli FU Yan MENG Dachun YANG | 2007 | Chinese Annals of Mathematics,Series B2007，28，1： | 3 |
| 19 | THE WEIGHTED HERZ-TYPE HARDY SPACES hK_q^(α,p)(ω_1,ω_2)显示文摘Let (.the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces (w2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show that , the class of C(Rn)-functions with compactly support, is dense in and there is a subsequence, which converges in distrbutional sense to some distribution of , of any bounded sequence in In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness. | Fan Dashan and Yang Dachun (University of WI~Milwaukee, U. S. A. and Beijing Normal University, China) | 1997 | Analysis in Theory and Applications1997，13，4： | 2 |
| 20 | Boundedness of Multilinear Operators in Herz-type Hardy Space | Lin Tang Dachun Yang Department of Mathematics,Beijing Normal University,Beijing 100875,P.R.China | 2000 | Acta Mathematica Sinica,English Series2000，16，2： | 2 |
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