Local approximations and intrinsic characterizations of spaces of smooth functions on regular subsets of $R^n$

TL;DR

This paper provides an intrinsic way to characterize various smooth function spaces on regular subsets of R^n using sharp maximal functions and local approximations, enhancing understanding of their structure.

Contribution

It introduces a novel intrinsic characterization of Sobolev, Triebel-Lizorkin, and Besov spaces on regular subsets of R^n based on sharp maximal functions and local approximations.

Findings

Characterization of function spaces via sharp maximal functions

Use of local approximations for intrinsic descriptions

Applicable to regular subsets of R^n

Abstract

We give an intrinsic characterization of the restrictions of Sobolev, Triebel-Lizorkin and Besov spaces to regular subsets of $R^n$ via sharp maximal functions and local approximations.