SOME MULTI-SUBLINEAR OPERATORS ON GENERALIZED MORREY SPACES WITH NON-DOUBLING MEASURES

2012 ◽  
Vol 49 (5) ◽  
pp. 907-925 ◽  
Author(s):  
Yanlong Shi ◽  
Xiangxing Tao
Keyword(s):  
Morrey Spaces ◽  
Generalized Morrey Spaces ◽  
Sublinear Operators ◽  
Doubling Measures

scholarly journals Sublinear operators with rough kernel on generalized Morrey spaces

1998 ◽  
Vol 27 (1) ◽  
pp. 219-232 ◽  
Author(s):  
Shanzhen LU ◽  
Dachun YANG ◽  
Zusheng ZHOU
Keyword(s):  
Morrey Spaces ◽  
Rough Kernel ◽  
Generalized Morrey Spaces ◽  
Sublinear Operators

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

2011 ◽  
Vol 71 (3) ◽  
pp. 327-355 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Seymur S. Aliyev ◽  
Turhan Karaman ◽  
Parviz S. Shukurov
Keyword(s):  
Morrey Spaces ◽  
Generalized Morrey Spaces ◽  
Sublinear Operators

scholarly journals Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Seymur S. Aliyev ◽  
Turhan Karaman
Keyword(s):  
Pseudodifferential Operators ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Sublinear Operator ◽  
Generalized Morrey Space ◽  
Riesz Operator ◽  
Generalized Morrey Spaces ◽  
Marcinkiewicz Operator ◽  
Sublinear Operators ◽  
Type Integral

The authors study the boundedness for a large class of sublinear operatorTgenerated by Calderón-Zygmund operator on generalized Morrey spacesMp,φ. As an application of this result, the boundedness of the commutator of sublinear operatorsTaon generalized Morrey spaces is obtained. In the casea∈BMO(ℝn),1<p<∞andTais a sublinear operator, we find the sufficient conditions on the pair (φ1,φ2) which ensures the boundedness of the operatorTafrom one generalized Morrey spaceMp,φ1to anotherMp,φ2. In all cases, the conditions for the boundedness ofTaare given in terms of Zygmund-type integral inequalities on (φ1,φ2), which do not assume any assumption on monotonicity ofφ1,φ2inr. Conditions of these theorems are satisfied by many important operators in analysis, in particular pseudodifferential operators, Littlewood-Paley operator, Marcinkiewicz operator, and Bochner-Riesz operator.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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