Vol. 15, No. 1, 2022

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Besov-ish spaces through atomic decomposition

Daniel Smania

Vol. 15 (2022), No. 1, 123–174
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