scholarly journals Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Guoen Hu ◽  
Haibo Lin ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Operator ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Littlewood Maximal Operator

WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

Calderón–Zygmund operators on multiparameter Lipschitz spaces of homogeneous type

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shaoyong He ◽  
Jiecheng Chen
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Main Tool ◽  
Weak Sense ◽  
Singular Integral Operators ◽  
Space Of Homogeneous Type ◽  
Factor Space ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lipschitz Spaces

Abstract The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of general product singular integral operators introduced by Han, Li and Lin [Y. Han, J. Li and C.-C. Lin, Criterion of the L 2 L^{2} boundedness and sharp endpoint estimates for singular integral operators on product spaces of homogeneous type, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 2016, 3, 845–907] on the multiparameter Lipschitz spaces of homogeneous type M ~ = M 1 × ⋯ × M n {\tilde{M}=M_{1}\times\cdots\times M_{n}} . Each factor space M i {M_{i}} , 1 ≤ i ≤ n {1\leq i\leq n} , is a space of homogeneous type in the sense of Coifman and Weiss. These operators generalize those studied by Journé on the Euclidean space and include operators studied by Nagel and Stein on Carnot–Carathéodory spaces. The main tool used here is the discrete Littlewood–Paley–Stein theory and almost orthogonality together with a density argument for the product Lipschitz spaces in the weak sense.

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