Abstract
An RD-space $(X, d,\mu)$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. An important class of RD-spaces is provided by Carnot-Caratheodory spaces with a doubling measure. In this article, the author establishes the embedding theorem for Besov and Triebel-Lizorkin spaces on RD-spaces.
Highlights
Introduction and statement of main resultsSpaces of homogeneous type, including metric measure spaces, play a prominent role in many fields of mathematics
Spaces of homogeneous type were introduced by Coifman and Weiss in the early s, in [ ]
In [ ], motivated by the work of Nagel and Stein, Besov and Triebel-Lizorkin spaces were developed on spaces of homogeneous type with a regular quasi-metric and a measure satisfying the reverse doubling condition, that is, there are constants κ ∈ (, ω] and c ∈ (, ] such that cλκ μ B(x, r) ≤ μ B(x, λr) for all x ∈ X, < r < supx,y∈X d(x, y)/ and ≤ λ < supx,y∈X d(x, y)/ r
Summary
Introduction and statement of main resultsSpaces of homogeneous type, including metric measure spaces, play a prominent role in many fields of mathematics. We say that (X, d, μ) is a space of homogeneous type in sense of Coifman and Weiss if d is a quasi-metric and μ is a nonnegative Borel regular measure on X satisfying the doubling condition, that is, for all x ∈ X, r > , < μ(B(x, r)) < ∞ and μ B(x, r) ≤ Cμ B(x, r) ,
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