Atomic and molecular decompositions of anisotropic Besov spaces

By Marcin Bownik. 2005

126 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dcd97e388ee32142dfe4c9c87d4f88ee8c84effb

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In Applied Mathematics

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Citations in the corpus

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.”
Anisotropic Triebel-Lizorkin spaces with doubling measures (2007, methodology): “Among other things proved in [ 3 , 5], weighted anisotropic Triebel-Lizorkin and Besov spaces are characterized by their wavelet transform coefficients and smooth atomic and molecular decompositions of these spaces are established.”
New Besov-type spaces and Triebel–Lizorkin-type spaces including Q spaces (2010, result): “generalize the classical results in [ 4 ,6,18,19] in the sense that if τ = 0, all these results are just the known results on ˙ B s, q (R n ) and ˙ F s p, q (R n ) therein.”
Coorbit spaces and wavelet coefficient decay over general dilation groups (2012, background): “In a similar way, the anisotropic Besov space studied in [3] can be read as coorbit spaces associated to cyclic or one-parameter dilation groups.”
Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases (2011, result): “Recent works are due to ROUDENKO [15, 39, 40] and BOWNIK [2, 3].”
Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces (2005, result): “Finally, we remark that an alternative proof of Lemma 3.1, which also works for doubling measures with respect to ρA (hence, a larger class than A∞ weights), can be found in [ 7 ].”
Frame Decomposition of Decomposition Spaces (2007, background): “From this point of view, the frame expansion (3.13) should perhaps be considered an adaptable variant of the ϕ-transform of Frazier and Jawerth [29, 28], see also the generalization in [8, 7 ].”
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].”
Entropy and Approximation Numbers of Embeddings of Function Spaces with Muckenhoupt Weights, I (2008, methodology): “Recent works are due to Roudenko [15,31,32] and Bownik [1, 2].”
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 [9, 8].”
New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets (2011, methodology): “Notice that we use more general biorthogonal wavelet bases instead of classical orthogonal wavelet bases as it is done for instance in [50, Chapter 3], in case of inhomogeneous classical Besov and Triebel-Lizorkin spaces, and also in [23, 26, 27, 28, 8, 9, 35].”
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].”