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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

An abstract theory of singular operators


Author: Grigori A. Karagulyan
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 42B20, 42B25; Secondary 43A85
DOI: https://doi.org/10.1090/tran/7722
Published electronically: February 25, 2019
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Abstract: We introduce a class of operators on abstract measure spaces that unifies the Calderón-Zygmund operators on spaces of homogeneous type, the maximal functions, the martingale transforms, and Carleson operators. We prove that such operators can be dominated by simple sparse operators with a definite form of the domination constant. Applying these estimates, we improve on several results obtained by different authors in recent years.


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Additional Information

Grigori A. Karagulyan
Affiliation: Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian Street, 0025 Yerevan, Armenia
Email: g.karagulyan@ysu.am

DOI: https://doi.org/10.1090/tran/7722
Keywords: Calder\'on--Zygmund operator, weighted inequalities, sparse operators, maximal function, martingale transform, homogeneous spaces
Received by editor(s): August 4, 2017
Received by editor(s) in revised form: April 21, 2018, and September 27, 2018
Published electronically: February 25, 2019
Article copyright: © Copyright 2019 American Mathematical Society