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

• Main Authors: Georgiadis Athanasios G., Kyriazis George
• Format: Article
• Language: English
• Published: De Gruyter 2020-01-01
• Series: Analysis and Geometry in Metric Spaces
• Subjects: besov spaces; distributions; doubling volume property; embeddings; heat kernel; metric spaces; triebel-lizorkin spaces; primary: 58j35, 58j40; secondary: 42b35, 42b25, 42b15, 46f10
• Online Access: https://doi.org/10.1515/agms-2020-0120
• ISSN: 2299-3274

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.