In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our...In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.展开更多
Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ（｜α｜= m）, The continuity of the operator on some Hardy and Herz type Hardy is obtained.
We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maxima...We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.展开更多
In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essential...In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.展开更多
As the extension of classical Hardy operator and Cesaro operator,Hausdorff operator plays an important role in the harmonic analysis,so it is significant to discuss the boundedness of this kind of operator on various ...As the extension of classical Hardy operator and Cesaro operator,Hausdorff operator plays an important role in the harmonic analysis,so it is significant to discuss the boundedness of this kind of operator on various function spaces.The article explores the boundedness of a kind of Hausdorff operators on Lebesgue spaces and calculates the optimal constants for the operators to be bounded on such spaces.In addition,the paper also obtains the necessary and sufficient for a kind of multilinear Hausdorff operators to be bounded on Lebesgue spaces and their optimal constants.展开更多
In this paper, we obtain the boundedness of multilinear Calderón-Zygmund operators with kernels of Dini type and commutators with variable exponent λ-central BMO functions in variable exponent central Morrey spa...In this paper, we obtain the boundedness of multilinear Calderón-Zygmund operators with kernels of Dini type and commutators with variable exponent λ-central BMO functions in variable exponent central Morrey spaces.展开更多
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p（R^n） to L^p（R^n） when the m-th order derivatives of A bel...In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p（R^n） to L^p（R^n） when the m-th order derivatives of A belong to L^p（R^n） for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are （L^p, L^p）-type operators for 1 〈 p 〈 ∞.展开更多
Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights f...Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.展开更多
The aim of this paper is to give a simple proof of the restriction theorem for the maximal operators on the d-dimensional Euclidean space Ra, whose theorem was proved by Carro-Rodriguez in 2012. Moreover, we shall giv...The aim of this paper is to give a simple proof of the restriction theorem for the maximal operators on the d-dimensional Euclidean space Ra, whose theorem was proved by Carro-Rodriguez in 2012. Moreover, we shall give some remarks of the restriction theorem for the linear and the multilinear operators by Carro-Rodriguez and Rodriguez, too.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10701010) the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry+1 种基金supported by National Natural Science Foundation of China (Grant No.10571015) Research Fund for the Doctoral Program of Higher Education of China (Grant No.20050027025)
文摘In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
基金Supported by RFDP of China (Grant No. 20050027025)NSF of China (Grant No. 10571014, 10571015)
文摘In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.
文摘Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ（｜α｜= m）, The continuity of the operator on some Hardy and Herz type Hardy is obtained.
基金Consejo Nacional de Investigaciones Científicas y Técnicas de la República ArgentinaUniversidad Nacional del Litoral
文摘We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.
基金supported by the National Natural Science Foundation of China(Nos.11871101,12171399)NSFC-DFG(No.11761131002)+3 种基金the Natural Science Foundation of Fujian Province(No.2021J05188)the Scientific Research Project of The Education Department of Fujian Province(No.JAT200331)the President’s fund of Minnan Normal University(No.KJ2020020)the Institute of Meteorological Big Data-Digital Fujian,Fujian Key Laboratory of Data Science and Statistics and Fujian Key Laboratory of Granular Computing and Applications(Minnan Normal University)。
文摘In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.
文摘As the extension of classical Hardy operator and Cesaro operator,Hausdorff operator plays an important role in the harmonic analysis,so it is significant to discuss the boundedness of this kind of operator on various function spaces.The article explores the boundedness of a kind of Hausdorff operators on Lebesgue spaces and calculates the optimal constants for the operators to be bounded on such spaces.In addition,the paper also obtains the necessary and sufficient for a kind of multilinear Hausdorff operators to be bounded on Lebesgue spaces and their optimal constants.
文摘In this paper, we obtain the boundedness of multilinear Calderón-Zygmund operators with kernels of Dini type and commutators with variable exponent λ-central BMO functions in variable exponent central Morrey spaces.
文摘In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p（R^n） to L^p（R^n） when the m-th order derivatives of A belong to L^p（R^n） for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are （L^p, L^p）-type operators for 1 〈 p 〈 ∞.
基金National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.
基金supported partly by Grant-in-Aid for Scientific Research(C)
文摘The aim of this paper is to give a simple proof of the restriction theorem for the maximal operators on the d-dimensional Euclidean space Ra, whose theorem was proved by Carro-Rodriguez in 2012. Moreover, we shall give some remarks of the restriction theorem for the linear and the multilinear operators by Carro-Rodriguez and Rodriguez, too.
