Vector-valued maximal multilinear Calderón–Zygmund operator with nonsmooth kernel on weighted Morrey space

He, Suixin; Zhou, Jiang

doi:10.1007/s11868-016-0169-5

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…The theory of Calderón-Zygmund operators, which has played very important roles in modern harmonic analysis with lots of extensive applications in the others elds of mathematics, has been extensively studied (see [1][2][3][4][5][6], for instance). In 1985, Yabuta introduced certain θ-type Calderón-Zygmund operators to facilitate his study of certain classes of pseudodi erential operators (see [7]).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

Yang

Tao

2018

Open Mathematics

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The aim of this paper is to deal with the boundedness of the θ-type Calderón-Zygmund operators and their commutators on Herz spaces with two variable exponents p(⋅), q(⋅). It is proved that the θ-type Calderón-Zygmund operators are bounded on the homogeneous Herz space with variable exponents $\begin{array}{} \displaystyle \dot{K}^{\alpha,q(\cdot)}_{p(\cdot)}(\mathbb{R}^{n}). \end{array}$ Furthermore, the boundedness of the corresponding commutators generated by BMO function and Lipschitz function is also obtained respectively.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

Yang

Tao

2018

Open Mathematics

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“…In 2009, Komori and Shirai [14] introduced the weighted Morrey spaces and study the several properties of classical operators on the classical Euclidean space. The further research and development about the Morrey spaces and weighted Morrey spaces over different settings, the readers can see [1,5,6,7,12,21,22,23,24,25] and the references therein. In 2020, Chou et al [4] introduced the generalized weighted Morrey spaces over RD-spaces, as applications, the boundedness of the classical operator was established.…”

Section: Introductionmentioning

confidence: 99%

Bilinear $θ$-type Calderón-Zygmund operators and its commutator on generalized weighted Morrey spaces over RD-spaces

He¹,

Tao²

2022

Preprint

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An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in X . In this setting, the authors establish the boundedness of bilinear θ-type Calderón-Zygmund operator T θ and its commutator [b 1 , b 2 , T θ ] generated by the function b 1 , b 2 ∈ BM O(µ) and T θ on generalized weighted Morrey space M p,φ (ω) and generalized weighted weak Morrey space W M p,φ (ω) over RD-spaces.

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The multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces

Cen

2023

Indian J Pure Appl Math

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Vector-valued maximal multilinear Calderón–Zygmund operator with nonsmooth kernel on weighted Morrey space

Cited by 5 publications

References 27 publications

θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

Bilinear $θ$-type Calderón-Zygmund operators and its commutator on generalized weighted Morrey spaces over RD-spaces

The multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces

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