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.

中文翻译：

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Triebel-Lizorkin 空间在与算子关联的度量空间上的嵌入

摘要 我们考虑了满足倍增体积特性的度量空间的一般框架，与非负自伴随算子相关联，其热核享受标准高斯定位。我们证明了与运算符相关的 Triebel-Lizorkin 空间之间的嵌入定理。非经典 Triebel-Lizorkin 和（经典和非经典）Besov 空间的嵌入也得到了证明。我们的结果概括了欧几里得情况，并且对于许多具有独立兴趣的设置（例如球、区间和黎曼流形）来说是新的。