Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces

By Marcin Bownik, Kwok-Pun Ho. 2005

187 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/7e82f7a7ed1192c1441e9709675a9975ca14bae1

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators (2008, background): “However, Meyer [25, p. 513] (see also [ 3 ,19]) gave an example off 2H1NRnO whose norm cannot be achieved by its finite atomic decompositions viaN1;1; 0Oatoms.”
Atomic and molecular decompositions of anisotropic Besov spaces (2005, methodology): “Almost diagonal operators on ˙ α,q p spaces for expansive dilations were introduced by the author and Ho [ 4 ].”
Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis (2008, background): “Results for (anisotropic) weighted Besov and Triebel–Lizorkin spaces, concerning the action of the φ-transform as well as atomic and molecular decomposition results for homogeneous and inhomogeneous spaces can be found in [2], [3].”
New Besov-type spaces and Triebel–Lizorkin-type spaces including Q spaces (2010, methodology): “With Lemmas 3.2–3.4, the proof of Theorem 3.1 follows the method pioneered by Frazier and Jawerth (see [18, pp.50–51]); see also the proof of [ 6, Theorem 3.5 ].”
Anisotropic Triebel-Lizorkin spaces with doubling measures (2007, methodology): “The goal of this work is to show that one can also build a coherent theory of weighted anisotropic Triebel-Lizorkin spaces associated with expansive dilations and doubling weights further generalizing the results of [ 5 , 20].”
Duality and interpolation of anisotropic Triebel–Lizorkin spaces (2008, background): “We prove that the expected isotropic results of Frazier and Jawerth [19] generalize to the non-isotropic setting.”
Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, methodology): “For more progresses about the theory of anisotropic function spaces on R, we refer the reader to [11, 25, 45, 48, 49, 51, 53, 54, 55] for anisotropic Hardy-type spaces and to [7, 8, 9, 46, 47, 56] for anisotropic Besov and TriebelLizorkin spaces.”
Wavelet transforms for homogeneous mixed-norm Triebel–Lizorkin spaces (2016, methodology): “4 was first stated by Bownik and Ho [8].”
Anisotropic Hardy-Lorentz spaces and their applications (2015, background): “For further developments of function spaces on the anisotropic Euclidean spaces, we refer the reader to [11, 12, 13, 24, 40, 41, 42, 71].”
On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators (2008, background): “Their results were generalized recently by Bownik and Ho to the anisotropic case [8, 7].”
A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions☆ (2009, background): “The almost diagonal operators were introduced by Frazier and Jawerth [13] and proved to be a very powerful tool therein (see also [8]).”
ENTROPY AND APPROXIMATION NUMBERS OF EMBEDDINGS OF FUNCTION SPACES WITH MUCKENHOUPT WEIGHTS, II. GENERAL WEIGHTS (2011, unknown): “Recent works are due to ROUDENKO [29, 30, 13], and BOWNIK [1, 2].”
Pseudodifferential operators on mixed‐norm Besov and Triebel–Lizorkin spaces (2016, background): “3 In [12] Bownik and Ho introduced Triebel–Lizorkin spaces based on dilations induced by expansive matrices.”