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| 1 | Endpoint estimates for n-dimensional Hardy operators and their commutators显示文摘In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed. | ZHAO FaYou FU ZunWei LU ShanZhen | 2012 | Science China Mathematics2012，55，10： | 19 |
| 2 | Commutators of n-dimensional rough Hardy operators显示文摘In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed. | FU ZunWei LU ShanZhen ZHAO FaYou | 2011 | Science China Mathematics2011，54，1： | 7 |
| 3 | Boundedness for commutators of fractional Hardy operators on Herz spaces显示文摘一些围住的海角结果为古典部分强壮的操作符和片面 CMO 函数在同类的 Herz 空格产生的整流器被建立,它扩大一些已知的结果。 | FU Zunwei LIU Zongguang LU Shanzhen | 2007 | Progress in Natural Science:Materials International2007，17，1： | 5 |
| 4 | Sharp estimates for Hardy operators on Heisenberg group显示文摘在海森堡组的设置,基于旋转方法,我们获得锋利(p, p ) 为强壮的操作符的估计。L p ( n ) 上的强壮的操作员的标准仍然是 p/(p-1 ) ,这将被显示出。这去暗示尽管有领域,强壮的操作员的 L p 标准是一样的某方法是间隔在上,在海森堡上的 n , 或椭圆体的球组织 n 。由构造一个特殊函数,我们在弱类型发现最好的常数(1, 1 ) 为强壮的操作符的不平等。用翻译途径,我们从 H 1 为强壮的操作员建立固定到 L 1 。而且,我们描述 M p 重量和 A p 重量之间的差别并且用加权的强壮的不平等获得如此的重量的描述。 | Qingyan WU Zunwei FU | 2016 | Frontiers of Mathematics in China2016，11，1： | 3 |
| 5 | Riesz-Kolmogorov theorem in variable exponent Lebesgue spaces and its applications to Riemann-Liouville fractional differential equations显示文摘In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-H¨older continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces. | Baohua Dong Zunwei Fu Jingshi Xu | 2018 | Science China Mathematics2018，61，10： | 2 |
| 6 | Commutators of weighted Hardy-Littlewood average operators显示文摘 | Fu Zunwei Liu Zongguang Lu Shanzhen | | (Preprint)0，，： | 1 |
| 7 | Weighted estimates for bilinear square functions with non-smooth kernels and commutators显示文摘Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions(with symbols which are BMO functions and their weighted version,respectively)on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley^-functions. | Rui BU Zunwei FU Yandan ZHANG | 2020 | Frontiers of Mathematics in China2020，15，1： | 1 |
| 8 | Compactness of the Commutators of Fractional Hardy Operator with Rough Kernel显示文摘The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central BMO(R^(n))-closure of C^(∞)(R^(n))space via the compactness of the commutators of fractional Hardy operator with rough kernel. | Shaoguang Shi Zunwei Fu | 2021 | Analysis in Theory and Applications2021，37，3： | 0 |
| 9 | Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces显示文摘We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case. | Feng LIU Zunwei FU Seong Tae JHANG | 2019 | Frontiers of Mathematics in China2019，14，1： | 0 |
| 10 | Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces显示文摘We study the Cauchy problem of a two-species chemotactic model. Using the Fourier frequency localization and the Bony paraproduct decomposition, we establish a unique local solution and blow-up criterion of the solution, when the initial data(u0, v0, w0) belongs to homogeneous Besov spaces˙B^(-2+3/p)_(p,1)(R^3) ×˙B^(-2+3/r)_(r,1)(R^3) ×˙B^(3/q)_(q,1)(R^3) for p, q and r satisfying some technical assumptions. Furthermore, we prove that if the initial data is sufficiently small, then the solution is global. Meanwhile, based on the so-called Gevrey estimates, we particularly prove that the solution is analytic in the spatial variable. In addition, we analyze the long time behavior of the solution and obtain some decay estimates for higher derivatives in Besov and Lebesgue spaces. | YANG MingHua FU ZunWei SUN JinYi | 2017 | Science China Mathematics2017，60，10： | 0 |
| 11 | Commutators of maximal functions on spaces of homogeneous type and their weighted,local versions显示文摘We obtain the characterizations of commutators of several versions of maximal functions on spaces of homogeneous type.In addition,with the aid of interpolation theory,we provide weighted version of the commutator theorems by establishing new characterizations of the weighted BMO space.Finally,a concrete example shows that the local version of commutators also has an independent interest. | Zunwei FU Elodie POZZI Qingyan WU | 2022 | Frontiers of Mathematics in China2022，17，4： | 0 |
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