TY - JOUR T1 - Partial Derivatives, Singular Integrals and Sobolev Spaces in Dyadic Settings AU - Aimar , Hugo AU - Comesatti , Juan AU - Gόmez , Ivana AU - Nowak , Luis JO - Analysis in Theory and Applications VL - 3 SP - 287 EP - 298 PY - 2023 DA - 2023/09 SN - 39 DO - http://doi.org/10.4208/ata.OA-2021-0051 UR - https://global-sci.org/intro/article_detail/ata/22002.html KW - Sobolev regularity, Haar basis, space of homogeneous type, Calderόn-Zygmund operator, dyadic analysis. AB -

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.