In this paper, we establish two integral inequalities for Hardy operator＇s conjugate operator at the endpoint on n-dimensional space. The operator Hn is bounded from Lxα1 （Gn） to Lxβq （Gn） with the bound explic...In this paper, we establish two integral inequalities for Hardy operator＇s conjugate operator at the endpoint on n-dimensional space. The operator Hn is bounded from Lxα1 （Gn） to Lxβq （Gn） with the bound explicitly worked out and the similar result holds for Hn＊.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.
In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β...In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).展开更多
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 in part by the Natural Science Foundation of China under grant 11071250 and 11271162
文摘In this paper, we establish two integral inequalities for Hardy operator＇s conjugate operator at the endpoint on n-dimensional space. The operator Hn is bounded from Lxα1 （Gn） to Lxβq （Gn） with the bound explicitly worked out and the similar result holds for Hn＊.
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Supported by the National Natural Science Foundation of China(Grant No.11661075).
文摘In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).
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.
