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 - <p style="text-align: justify;">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.</p>