A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions☆

By Pekka Koskela, Dachun Yang, Yuan Zhou. 2009

74 citations recorded by the source corpus.

Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/9357f85a6149a1d162e2b5c49b96195f53f27c18

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In Applied Mathematics

Citations in the corpus

Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces (2011, background): “For the pointwise characterization Ṁ s p, q(X ) = Ḟ s p, q(X ) on a metric measure space satisfying doubling and reverse doubling properties, when s ∈ (0, 1) and p, q ∈ (n/(n + s), ∞], see [18, 19]; also see [9, 6, 21] for some other characterizations.”
Multilinear analysis on metric spaces (2014, background): “RD-spaces have become the underlying context in numerous areas of analysis and PDEs, we refer the reader to [22, 23], [60, 61, 86], [71, 72, 40], [107, 109, 108] and references therein.”
Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings (2010, unknown): “Motivated by [22], when μ(X ) = ∞, for all x ∈ X and k ∈ Z, let (4.”
A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type (2018, unknown): “More on analysis over Ahlfors-n regular metric measure spaces or RD-spaces can be found in [18, 22, 33, 34, 52, 32, 55, 8, 56].”