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A unified method for maximal truncated Calderón–Zygmund operators in general function spaces by sparse domination

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  22 November 2019

Theresa C. Anderson  and
Bingyang Hu
Theresa C. Anderson
Affiliation:
Department of Mathematics, Purdue University, 150 N, University St., West Lafayette, IN47907, USA ([email protected])
Bingyang Hu
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, 480 Lincoln Dr., Madision, WI53705, USA ([email protected])
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Abstract

In this note we give simple proofs of several results involving maximal truncated Calderón–Zygmund operators in the general setting of rearrangement-invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to track the dependence of the constants in weighted norm inequalities; additionally, our results hold in ℝn as well as in many spaces of homogeneous type.

Keywords

sparse dominationweighted inequalitiesBanach function spacesmaximal truncations

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 1 , February 2020 , pp. 229 - 247
Copyright
Copyright © Edinburgh Mathematical Society 2019

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