Continuity of Multilinear Operators in Weighted Herz Spaces with Extreme Exponents

Continuity is obtained of some multilinear operators related to certain integral operators for the weighted Herz spaces with extreme exponents. The operators include the Littlewood–Paley and Marcinkiewicz operators.     

Some BMO estimates for vector-valued multilinear singular integral operators

In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators.     

Sharp weighted inequality for a multilinear commutator of the Marcinkiewicz operator

A sharp inequality for a multilinear commutator related to the Marcinkiewicz operator is proved. As a consequence, weighted L^p-norm inequality for the multilinear commutator for 1 < p < ∞ is obtained. Bibliography: 12 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 86–97.     

Boundednes of Singular Integral Operators On Some Atom Spaces

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齐型空间上算子的加权内插及其应用

本文在齐型空间上建立了算子的加权情形下的实内插定理，运用该结果，立即可推导出齐型空间上Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ算子的加权Ｌ^ｐ有界性（ｐ＞１）和弱Ｌ¹有界性。     

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations ∑in, j=1 aijuxixj = f,if f belongs to the generalized Morrey spaces Lp,ψ(ω), then uxixj ∈ Lp,ψ(ω), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp,ψ (ω).     

Weighted boundedness for multilinear Littlewood-Paley and Marcinkiewicz operators on Morrey spaces

Some sharp estimates for multilinear operators are used to prove weighted boundedness of the multilinear Littlewood-Paley and Marcinkiewicz operators on the Morrey spaces.     

The Continuity of Commutators on Triebel-Lizorkin Spaces

The purpose of this paper is to study the continuity in the context of Triebel-Lizorkin spaces for some commutators related to certain convolution operators. The operators include Littlewood-Paley operator, Marcinkiewicz integral and Bochner-Riesz operator.     

平均振荡和相关于具有非光滑核的奇异积分算子的Toeplitz型算子的有界性

对相关于具有非光滑核的奇异积分算子的Toeplitz型算子,证明了其从Lebesgue空间到Orlicz空间的有界性.     

Necessary and sufficient conditions for boundedness of commutators of strongly singular integral operators with weighted Lipschitz functions

In this paper, we prove the commutator T _b generated by the strongly singular integral operator T and the function b is bounded from L ^p (w) to L ^q (w ^1−q ) if and only if b ∈ Lip _β (w), where w ∈ A ₁, 0 < β < 1, 1 < p < n/β and 1/q = 1/p − β/n. To do this, we first show a maximal function estimate for the commutator.