scholarly journals Stability of integral operators on a space of homogeneous type

2016 ◽  
Vol 290 (2-3) ◽  
pp. 284-292 ◽  
Author(s):  
Qiquan Fang ◽  
Chang Eon Shin
Keyword(s):  
Integral Operators ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type

scholarly journals Sharp Weighted Bounds for Fractional Integral Operators in a Space of Homogeneous Type

2014 ◽  
Vol 114 (2) ◽  
pp. 226 ◽  
Author(s):  
Anna Kairema
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Operator Norm ◽  
Fractional Integral Operator ◽  
Weighted Spaces ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Fractional Integral Operators ◽  
The Relationship

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy-Littlewood-Sobolev theorem in this context. In our main result, we investigate the dependence of the operator norm on weighted spaces on the weight constant, and find the relationship between these two quantities. It it shown that the estimate obtained is sharp in any given space of homogeneous type with infinitely many points. Our result generalizes the recent Euclidean result by Lacey, Moen, Pérez and Torres [21].

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.

scholarly journals FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

2009 ◽  
Vol 80 (2) ◽  
pp. 324-334 ◽  
Author(s):  
H. GUNAWAN ◽  
Y. SAWANO ◽  
I. SIHWANINGRUM
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Homogeneous Type ◽  
Fractional Integral Operators

AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

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.

scholarly journals Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type

2016 ◽  
Vol 27 (1) ◽  
pp. 95-119 ◽  
Author(s):  
Theresa C. Anderson ◽  
Tuomas Hytönen ◽  
Olli Tapiola
Keyword(s):  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Reverse Hölder

scholarly journals A Variant of the Notion of a Space of Homogeneous Type

1995 ◽  
Vol 132 (1) ◽  
pp. 119-140 ◽  
Author(s):  
A. Carbery ◽  
J. Vance ◽  
S. Wainger ◽  
J. Wright
Keyword(s):  
Space Of Homogeneous Type ◽  
Homogeneous Type
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