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.

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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