Bilinear $$\theta $$-type Calderón–Zygmund operator and its commutator on non-homogeneous weighted Morrey spaces

2020 ◽  
Vol 115 (1) ◽  
Author(s):  
Guanghui Lu
Keyword(s):  
Morrey Spaces ◽  
Zygmund Operator ◽  
Weighted Morrey Spaces

scholarly journals Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

2014 ◽  
Vol 64 (2) ◽  
pp. 365-386 ◽  
Author(s):  
Vagif Sabir Guliyev ◽  
Turhan Karaman ◽  
Rza Chingiz Mustafayev ◽  
Ayhan Şerbetçi
Keyword(s):  
Morrey Spaces ◽  
Zygmund Operator ◽  
Weighted Morrey Spaces ◽  
Sublinear Operators

scholarly journals Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Bijun Ren ◽  
Enbin Zhang
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Linear Operators ◽  
Identity Operator ◽  
Zygmund Operator ◽  
Weighted Bmo ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Bmo Spaces ◽  
Toeplitz Type Operator

LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.

scholarly journals Multilinear Singular Integral Operators on Generalized Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Hu ◽  
Zhang Li ◽  
Yueshan Wang
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Zygmund Operator ◽  
Multilinear Singular Integral ◽  
Weighted Morrey Spaces

The purpose of this paper is to discuss the boundedness properties of multilinear Calderón-Zygmund operator and its commutator on the generalized weighted Morrey spaces.

scholarly journals Multilinear Commutators of Calderón-Zygmund Operator on Generalized Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Farida Ch. Alizadeh
Keyword(s):  
Weight Function ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Integral Inequalities ◽  
Zygmund Operator ◽  
Weighted Morrey Spaces ◽  
Type Integral ◽  
Multilinear Commutators

The boundedness of multilinear commutators of Calderón-Zygmund operatorTb→on generalized weighted Morrey spacesMp,φ(w)with the weight functionwbelonging to Muckenhoupt's classApis studied. When1<p<∞andb→=(b1,…,bm),bi∈BMO,i=1,…,m, the sufficient conditions on the pair(φ1,φ2)which ensure the boundedness of the operatorTb→fromMp,φ1(w)toMp,φ2(w)are found. In all cases the conditions for the boundedness ofTb→are given in terms of Zygmund-type integral inequalities on(φ1,φ2), which do not assume any assumption on monotonicity ofφ1(x,r),  φ2(x,r)inr.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

scholarly journals The Fractional Operators on Weighted Morrey Spaces

2017 ◽  
Vol 28 (2) ◽  
pp. 1502-1524 ◽  
Author(s):  
Shohei Nakamura ◽  
Yoshihiro Sawano ◽  
Hitoshi Tanaka
Keyword(s):  
Morrey Spaces ◽  
Fractional Operators ◽  
Weighted Morrey Spaces

scholarly journals The Boundedness of the Hardy-Littlewood Maximal Operator and Multilinear Maximal Operator in Weighted Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Takeshi Iida
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Morrey Spaces ◽  
Weighted Morrey Spaces ◽  
Type Spaces ◽  
Multilinear Maximal Function ◽  
Multilinear Maximal Operator ◽  
Littlewood Maximal Operator

The aim of this paper is to prove the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces and multilinear maximal operator on multiple weighted Morrey spaces. In particular, the result includes the Komori-Shirai theorem and the Iida-Sato-Sawano-Tanaka theorem for the Hardy-Littlewood maximal operator and multilinear maximal function.

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