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arXiv · 1611.03808

An abstract theory of singular operators

Grigori A. Karagulyan
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Abstract

We introduce a class of operators on abstract measure spaces, which unifies the Calder\'on-Zygmund operators on spaces of homogeneous type, the maximal functions and the martingale transforms. 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 several results obtained by different authors in recent years.

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Grigori A. Karagulyan. 2016-11-11. An abstract theory of singular operators. https://doi.org/10.1090/tran%2F7722

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