Partial Derivatives, Singular Integrals and Sobolev Spaces in Dyadic Settings

Partial Derivatives, Singular Integrals and Sobolev Spaces in Dyadic Settings

Year:    2023

Author:    Hugo Aimar, Juan Comesatti, Ivana Gόmez, Luis Nowak

Analysis in Theory and Applications, Vol. 39 (2023), Iss. 3 : pp. 287–298

Abstract

In this note we show that the general theory of vector valued singular integral operators of Calderόn-Zygmund defined on general metric measure spaces, can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian. In doing so, we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2021-0051

Analysis in Theory and Applications, Vol. 39 (2023), Iss. 3 : pp. 287–298

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Sobolev regularity Haar basis space of homogeneous type Calderόn-Zygmund operator dyadic analysis.

Author Details

Hugo Aimar

Juan Comesatti

Ivana Gόmez

Luis Nowak