Properties of parabolic Sobolev and parabolic Besov spaces

TL;DR

This paper characterizes parabolic Sobolev and Besov spaces in Euclidean space and studies their relationships, providing a detailed mathematical framework for understanding these function spaces in parabolic contexts.

Contribution

It offers new characterizations of parabolic Sobolev and Besov spaces and explores their connections with standard Besov spaces, advancing the theoretical understanding of these spaces.

Findings

Characterization of parabolic Sobolev spaces in ${f R}^{n+1}$ and ${f R}^{n+1}_T$

Characterization of parabolic Besov spaces in ${f R}^{n+1}$ and ${f R}^{n+1}_T$

Analysis of the relation between parabolic Besov spaces and standard Besov spaces

Abstract

In this paper, we characterize parabolic Besov and parabolic Sobolev spaces in ${\bf R}^{n+1}$ and ${\bf R}^{n+1}_T, \,\, T > 0$. We also, study the relation between parabolic Besov spaces in ${\bf R}^{n}_T, \,\, T > 0$ and standard Besov space in $\R$.