A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.

H.-Q. Bui; M. Paluszyński; M. Taibleson

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Displaying similar documents to “A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.”

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One-sided versions of maximal functions for suitable defined distributions are considered. Weighted norm equivalences of these maximal functions for weights in the Sawyer's Aq+ classes are obtained.

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We give characterizations of Besov and Triebel-Lizorkin spaces $B_{p q}^{s} (Ω)$ and $F_{p q}^{s} (Ω)$ in smooth domains $Ω \subset ℝ^{n}$ via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.

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