# A unified approach for Littlewood-Paley Decomposition of Abstract Besov Spaces

## TL;DR

This paper introduces a spectral theoretic method to unify Littlewood-Paley decompositions across various abstract Besov spaces, providing a general framework that encompasses well-known special cases.

## Contribution

It develops a unified spectral theoretic approach for Littlewood-Paley decomposition in abstract Besov spaces, extending and unifying existing specific decompositions.

## Key findings

- Unified spectral approach for Besov spaces
- Generalizes known Littlewood-Paley decompositions
- Applicable to various contexts and spaces

## Abstract

We apply spectral theoretic methods to obtain a Littlewood-Paley decomposition of abstract inhomogeneous Besov spaces in terms of "smooth" and "bandlimited" functions. Well-known decompositions in several contexts are as special examples and are unified under the spectral theoretic approach