# Besov-ish spaces through atomic decomposition

## TL;DR

This paper introduces new function spaces akin to Besov spaces using atomic decomposition in measure spaces with grids, providing insights into multipliers and compositions for low-regularity cases.

## Contribution

It develops a novel approach to constructing Besov-like spaces via atomic decomposition in measure spaces with minimal assumptions.

## Key findings

- New Besov-like spaces constructed using atomic decomposition.
- Results on multipliers for low-regularity spaces.
- Analysis of left compositions in the new spaces.

## 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 results on multipliers and left compositions are obtained.