Besov-ish spaces through atomic decomposition

Smania, Daniel

doi:10.2140/apde.2022.15.123

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Besov-ish spaces through atomic decomposition

Daniel Smania

Vol. 15 (2022), No. 1, 123–174

DOI: 10.2140/apde.2022.15.123

Abstract

We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good grids, and we obtain results on multipliers and left compositions in this setting.

Keywords

atomic decomposition, Besov space, harmonic analysis, wavelets, multipliers, Haar wavelets, atoms

Mathematical Subject Classification

Primary: 43A99, 43A85, 30H25, 42B15, 42B35, 42C15, 42C40, 28C99

Milestones

Received: 17 July 2019

Revised: 18 July 2020

Accepted: 15 September 2020

Published: 16 March 2022

Authors

Daniel Smania
Departamento de Matemática Instituto de Ciências Matemáticas e de Computação-Universidade de São Paulo (ICMC/USP) - São Carlos São Carlos Brazil

Vol. 15, No. 1, 2022