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arXiv · 2003.04019

Dyadic representation theorem using smooth wavelets with compact support

Tuomas Hytönen·Stefanos Lappas
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Abstract

The representation of a general Calder\'on--Zygmund operator in terms of dyadic Haar shift operators first appeared as a tool to prove the $A_2$ theorem, and it has found a number of other applications. In this paper we prove a new dyadic representation theorem by using smooth compactly supported wavelets in place of Haar functions. A key advantage of this is that we achieve a faster decay of the expansion when the kernel of the general Calder\'on--Zygmund operator has additional smoothness.

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Tuomas Hytönen, Stefanos Lappas. 2020-03-09. Dyadic representation theorem using smooth wavelets with compact support. https://doi.org/10.1007/s00041-022-09963-1

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