An abstract theory of singular operators

Karagulyan, Grigori

doi:10.1090/tran/7722

An abstract theory of singular operators
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by Grigori A. Karagulyan PDF

Trans. Amer. Math. Soc. 372 (2019), 4761-4803 Request permission

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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