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...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.展开更多
In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results a...In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.展开更多
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm ...In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.展开更多
In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bou...In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.展开更多
This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type （p,p） （1 〈 p 〈 ∞） estimates of n- dimensional Hausdorff operato...This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type （p,p） （1 〈 p 〈 ∞） estimates of n- dimensional Hausdorff operators on Hn are obtained. The sharp bounds for strong （p,p） estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hn. The weak type （p,p） （1 〈 p 〈 ∞） estimates are also obtained.展开更多
We calculate the sharp bounds for some q-analysis variants of Hausdorff type inequalities of the form As applications, we obtain several sharp q-analysis inequalities of the classical positive integral operators, incl...We calculate the sharp bounds for some q-analysis variants of Hausdorff type inequalities of the form As applications, we obtain several sharp q-analysis inequalities of the classical positive integral operators, including the Hardy operator and its adjoint operator, the Hilbert operator, and the Hardy-Littlewood-P61ya operator.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos. 10931001,10901076 and 11171345)Shanghai Leading Academic Discipline Project(Grant No.J50101)supported by the Key Laboratory of Mathematics and Complex System(Beijing Normal University),Ministry of Education,China
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.
基金supported by NSF of China(Grant Nos.10931001,10871173)supported by NSF of China(Grant No.11026104)
文摘In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
文摘In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.
基金supported by National Natural Science Foundation of China (Grant No.11871452)Beijing Information Science and Technology University Foundation (Grant No.2025031)+1 种基金Natural Science Foundation of Henan Province (Grant No.202300410338)the Nanhu Scholar Program for Young Scholars of Xinyang Normal University.
文摘In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.
基金Supported by National Natural Science Foundation of China(Grant No.11201287)China Scholarship Council(Grant No.201406895019)
文摘This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type （p,p） （1 〈 p 〈 ∞） estimates of n- dimensional Hausdorff operators on Hn are obtained. The sharp bounds for strong （p,p） estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hn. The weak type （p,p） （1 〈 p 〈 ∞） estimates are also obtained.
文摘We calculate the sharp bounds for some q-analysis variants of Hausdorff type inequalities of the form As applications, we obtain several sharp q-analysis inequalities of the classical positive integral operators, including the Hardy operator and its adjoint operator, the Hilbert operator, and the Hardy-Littlewood-P61ya operator.
