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

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.

Keywords

• besov spaces
• distributions
• doubling volume property
• embeddings
• heat kernel
• metric spaces
• triebel-lizorkin spaces
• primary: 58j35, 58j40
• secondary: 42b35, 42b25, 42b15, 46f10