For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equival...For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.展开更多
Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness o...Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the LP(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn)) boundedness for the corresponding commutators. A new interpolation theorem is also established.展开更多
Let Ф be a Young function and MФ be the maximal operator associated with in the space of homogeneous type. In this paper, the composition of the maximal operators of type MФ is considered, and the result establishe...Let Ф be a Young function and MФ be the maximal operator associated with in the space of homogeneous type. In this paper, the composition of the maximal operators of type MФ is considered, and the result established by Carrozza and Passarelli Di Napoli is generalized to the space of homogeneous type.展开更多
Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund o...Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund operators and maximal commutators which are variants of the usual maximal commutators generated by Calder6ón- Zygmund operators and RBMO（μ） functions, where the Hardytype spaces are some appropriate subspaces, associated with the considered RBMO（μ） functions, of the Hardv soace H^I（μ） of Tolsa.展开更多
Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the...Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.展开更多
The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderon-Zygmund singular integrals and Orlicz type functions with non-doubling measures.
Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some sizeconditions implying the Lp(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed1 ＜ p ＜∞ are ob...Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some sizeconditions implying the Lp(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed1 ＜ p ＜∞ are obtained.展开更多
基金Program for New Century Excellent Talents in University(NCET-04-0142)of China
文摘For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.
基金This research was supported by the NNSF of China (10271015)
文摘Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the LP(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn)) boundedness for the corresponding commutators. A new interpolation theorem is also established.
基金Supported by the NSF from the Education Department of Henan Province(2007110006)
文摘Let Ф be a Young function and MФ be the maximal operator associated with in the space of homogeneous type. In this paper, the composition of the maximal operators of type MФ is considered, and the result established by Carrozza and Passarelli Di Napoli is generalized to the space of homogeneous type.
基金Program for New Century Excellent Talents in University(NCET-04-0142)of China
文摘Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund operators and maximal commutators which are variants of the usual maximal commutators generated by Calder6ón- Zygmund operators and RBMO（μ） functions, where the Hardytype spaces are some appropriate subspaces, associated with the considered RBMO（μ） functions, of the Hardv soace H^I（μ） of Tolsa.
基金NNSF(No.10271015)of ChinaRFDP(No.20020027004)of China
文摘Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.
基金The research is supported by NNSFC (10271015)the third (corresponding) author is also supported by RFDPC (20020027004)
文摘The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderon-Zygmund singular integrals and Orlicz type functions with non-doubling measures.
基金This work was supported by the NSF of Henan Province, National 973 Project ofChina (G19990751) Prof. Xu Yuesheng's research grant in the program of "One Hundred Distinguished Young Scientists" of the Chinese Academy of Sciences.
文摘Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some sizeconditions implying the Lp(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed1 ＜ p ＜∞ are obtained.
