Weighted complete continuity for the commutator of Marcinkiewicz integral

Triebel--Lizorkin space estimates for multilinear operators of sublinear operators

In this paper, we obtain the continuity for some multilinear operators related to certain non-convolution operators on the Triebel--Lizorkin space. The operators include Littlewood--Paley operator and Marcinkiewicz operator.

Multilinear fractional type operators and their commutators on Hardy spaces with variable exponents

In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity properties of commutators of multilinear fractional type operators on product of certain Hardy spaces with variable exponents.

Operator and commutator moduli of continuity for normal operators

We study in this paper properties of functions of perturbed normal operators and develop earlier results obtained in \cite{APPS2}. We study operator Lipschitz and commutator Lipschitz functions on closed subsets of the plane. For such functions we introduce the notions of the operator modulus of continuity and of various commutator moduli of continuity. Our estimates lead to estimates of the norms of quasicommutators $f(N_1)R-Rf(N_2)$ in terms of $\|N_1R- RN_2\|$, where $N_1$ and $N_2$ are normal operator and $R$ is a bounded linear operator. In particular, we show that if $0<\a<1$ and $f$ is …

The boundedness of some operators with rough kernel on the weighted Morrey spaces

Let $Ω\in L^q(S^{n-1})$ with $1<q\le\infty$ be homogeneous of degree zero and has mean value zero on $S^{n-1}$. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces $L^{p,κ}(w)$ for $q'\le p<\infty$(or $q'<p<\infty$) and $0<κ<1$. We will also prove that the commutator operators formed by a $BMO(\mathbb R^n)$ function $b(x)$ and these rough operators are bounded on the weighted Morrey spaces $L^{p,κ}(w)$ for $q'<p<\infty$ and $0<κ<1$.

函数空间中多线性伪微分算子的定量加权估计

Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces

该研究系统推导了重排不变Banach与拟Banach空间中多线性伪微分算子及其交换子的加权有界性和模估计，并将结果推广至多线性Fourier乘子等三类算子。

Some extensions of classes involving pair of weights related to the boundedness of multilinear commutators associated to generalized fractional integral operators

We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_α^m$, from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces, extending some previous estimates for the linear case. Our study includes two different types of commutators and sufficient conditions on the weights in order to guarantee the continuity properties described above. We also exhibit the optimal range of the parameters involved. The optimality is understood in the sense that the parameters defini…

多线性设置中超越极值的 $\oldsymbol{p}$ 值相关的分数阶算子若干交换子的平滑性性质

Smoothness properties related to several commutators of fractional operators for values of $\boldsymbol{p}$ beyond the extreme in the multilinear setting

本文证明了多线性分数阶算子高阶交换子从加权 Lebesgue 空间乘积到加权 Lipschitz 空间的连续性，推广了无权和线性情形的估计，并完整分析了相关多线性权性质及最优参数区域。

Boundedness of fractional integral operators with rough kernels on weighted Morrey spaces

Let $M_{Ω,α}$ and $T_{Ω,α}$ be the fractional maximal and integral operators with rough kernels, where $0<α<n$. In this paper, we shall study the continuity properties of $M_{Ω,α}$ and $T_{Ω,α}$ on the weighted Morrey spaces $L^{p,κ}(w)$. The boundedness of their commutators with BMO functions is also obtained.

Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers

Let $T$ be a multilinear operator which is bounded on certain products of unweighted Lebesgue spaces of $\mathbb R^n$. We assume that the associated kernel of $T$ satisfies some mild regularity condition which is weaker than the usual Hölder continuity of those in the class of multilinear Calderón-Zygmund singular integral operators. We then show the boundedness for $T$ and the boundedness of the commutator of $T$ with BMO functions on products of weighted Lebesgue spaces of $\mathbb R^n$. As an application, we obtain the weighted norm inequalities of multilinear Fourier multipliers and of the…

Regularity and continuity of the multilinear strong maximal operators

Let $m\ge 1$, in this paper, our object of investigation is the regularity and and continuity properties of the following multilinear strong maximal operator $${\mathscr{M}}_{\mathcal{R}}(\vec{f})(x)=\sup_{\substack{R \ni x R\in\mathcal{R}}}\prod\limits_{i=1}^m\frac{1}{|R|}\int_{R}|f_i(y)|dy,$$ where $x\in\mathbb{R}^d$ and $\mathcal{R}$ denotes the family of all rectangles in $\mathbb{R}^d$ with sides parallel to the axes. When $m=1$, denote $\mathscr{M}_{\mathcal{R}}$ by $\mathcal {M}_{\mathcal{R}}$.Then, $\mathcal {M}_{\mathcal{R}}$ coincides with the classical strong maximal function initia…

乘积空间上紧性的二进分析

Dyadic analysis of compactness on product spaces

本研究采用现代视角建立乘积空间多线性奇异积分紧性理论，证明多线性紧性T1定理并给出交换子平均连续性结果，拓展了Journé定理的适用范围。