Besov classes on finite- and infinite-dimensional spaces and embedding theorems

TL;DR

This paper introduces a new way to describe Besov spaces using a novel modulus of continuity, extending the concept to infinite-dimensional Gaussian spaces.

Contribution

It provides a new characterization of Besov spaces and extends the framework to infinite-dimensional Gaussian measures.

Findings

New description of classical Besov spaces

Extension of Besov classes to infinite-dimensional spaces

Development of a new modulus of continuity

Abstract

We give a new description of classical Besov spaces in terms of a new modulus of continuity. Then a similar approach is used to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure.