In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
In this paper, the authors establish the Lp-mapping properties of a class of singular integral operators along surfaces of revolution with rough kernels. The size condition on the kernels is optimal and much weaker th...In this paper, the authors establish the Lp-mapping properties of a class of singular integral operators along surfaces of revolution with rough kernels. The size condition on the kernels is optimal and much weaker than that for the classical Calderon-Zygmund singular integral operators.展开更多
In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 〈 p 〈 ∞, the L^p-bound...In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 〈 p 〈 ∞, the L^p-boundedness of such operators are obtained provided that their kernels belong to the spaces L^q（s^n-1） for some q 〉 1.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
We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on IR+. which are closely related to the best constants of the weak type (1,1) estimates for such operators. Meanwhi...We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on IR+. which are closely related to the best constants of the weak type (1,1) estimates for such operators. Meanwhile, the corresponding results for Hardy-Littlewood maximal operator and fractional maximal operator in Bessel setting are also obtained.展开更多
The authors establish the boundedness of the variation operators associated with the heat semigroup, Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schr?dinger setting...The authors establish the boundedness of the variation operators associated with the heat semigroup, Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schr?dinger setting on the Morrey spaces.展开更多
This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition Fa（S^m-1 × S ...This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition Fa（S^m-1 × S ^n-1） of the kernel implies the L P-boundedness of these Marcinklewicz integral operators for 1 some a 〉 1/2 and 1 ＋ 1/2a 〈 p 〈 1 ＋ 2a, which is an essential improvement of certain previous results.展开更多
Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)...Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)belongs to the Orlicz space Osc_(exp L^(si)).展开更多
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
文摘In this paper, the authors establish the Lp-mapping properties of a class of singular integral operators along surfaces of revolution with rough kernels. The size condition on the kernels is optimal and much weaker than that for the classical Calderon-Zygmund singular integral operators.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771054)the Natural Science Foundation of Fujian Province of China (Grant No. Z0511004)
文摘In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 〈 p 〈 ∞, the L^p-boundedness of such operators are obtained provided that their kernels belong to the spaces L^q（s^n-1） for some q 〉 1.
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We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on IR+. which are closely related to the best constants of the weak type (1,1) estimates for such operators. Meanwhile, the corresponding results for Hardy-Littlewood maximal operator and fractional maximal operator in Bessel setting are also obtained.
基金supported by the National Natural Science Foundation of China(Nos.11771358,11471041)the Open Foundation of the “13th Five-Year” Discipline(Mathematics)of Xinjiang Uygur Autonomous Region(No.XJZDXK-M2017016)
文摘The authors establish the boundedness of the variation operators associated with the heat semigroup, Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schr?dinger setting on the Morrey spaces.
文摘This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition Fa（S^m-1 × S ^n-1） of the kernel implies the L P-boundedness of these Marcinklewicz integral operators for 1 some a 〉 1/2 and 1 ＋ 1/2a 〈 p 〈 1 ＋ 2a, which is an essential improvement of certain previous results.
文摘Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)belongs to the Orlicz space Osc_(exp L^(si)).
