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.