# Identification of Besov spaces via Littlewood-Paley-Stein Type g-functions

## TL;DR

This paper characterizes inhomogeneous abstract Besov spaces on Hilbert spaces using Littlewood-Paley-Stein g-functions, extending the theory to spaces defined via Poisson and Gauss-Weierstrass semigroups.

## Contribution

It provides a new characterization of Besov spaces through generalized square functions associated with symmetric diffusion semigroups.

## Key findings

- Characterization of inhomogeneous Besov spaces using g-functions
- Application to spaces defined by Poisson and Gauss-Weierstrass semigroups
- Extension of Littlewood-Paley theory to abstract Hilbert spaces

## Abstract

We use Littlewood-Paley-Stein type g-functions (also called generalized square functions) associated to symmetric diffusion semigroups to obtain a characterization of inhomogeneous abstract Besov spaces on the abstract Hilbert spaces. Then we apply our results for the abstract Besov spaces defined through the Poisson and Gauss-Weierstrass semigroups.