Embeddings between Triebel-Lizorkin Spaces on Metric Spaces Associated with Operators

Athanasios G. Georgiadis,George Kyriazis

doi:10.1515/agms-2020-0120

Abstract

Abstract We consider the general framework of a metric measure space satisfying the doubling volume property, associated with a non-negative self-adjoint operator, whose heat kernel enjoys standard Gaussian localization. We prove embedding theorems between Triebel-Lizorkin spaces associated with operators. Embeddings for non-classical Triebel-Lizorkin and (both classical and non-classical) Besov spaces are proved as well. Our result generalize the Euclidean case and are new for many settings of independent interest such as the ball, the interval and Riemannian manifolds.

Highlights

Function spaces play a leading role in analysis and its applications for almost a century
We consider the general framework of a metric measure space satisfying the doubling volume property, associated with a non-negative self-adjoint operator, whose heat kernel enjoys standard Gaussian localization
We prove embedding theorems between Triebel-Lizorkin spaces associated with operators

Summary

Introduction

Function spaces play a leading role in analysis and its applications for almost a century. We prove embedding theorems between Triebel-Lizorkin spaces associated with operators. Embeddings for non-classical Triebel-Lizorkin and (both classical and non-classical) Besov spaces are proved as well.

Results

Conclusion