Decomposition of Besov Spaces

By Michael Frazier, Björn-Martin Werth. 2009

409 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3a781f12c7ebf10439a2343f630d3ebabdcf9e84

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In Applied Mathematics

Citations in the corpus

On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators (2008, positive): “Frazier and Jawerth constructed frames (their so-called φ-transform) for Besov and T-L spaces in [20, 19].”
Frame Decomposition of Decomposition Spaces (2007, methodology): “13) should perhaps be considered an adaptable variant of the φ-transform of Frazier and Jawerth [25, 24], see also the generalization in [6, 5].”
A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions☆ (2009, methodology): “in S ′(Rn) and pointwise; see [12, 14] and also [8, Lemma 2.”
Atomic, molecular and wavelet decomposition of 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability (2010, background): “The next lemmas go back to Frazier & Jawerth [15] and a proof adapted to our setting can be found in [21].”
Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings (2011, background): “Let us recall the characterization of homogeneous Besov spaces Bσ p,q from [13], see also [16, 21].”
New Besov-type spaces and Triebel–Lizorkin-type spaces including Q spaces (2010, methodology): “Besov spaces [ 16 ,19,25,26], Triebel–Lizorkin spaces [18,19,25,26 ]a ndQ spaces [14 ]o n R n . Thus, we give a complete answer to the question of Dafni and Xiao in [8].”
Decomposition of Spaces of Distributions Induced by Hermite Expansions (2007, methodology): “of [5, 6] we will construct a pair of dual frames in terms of Hermite functions and use them to characterize the Hermite-Triebel-Lizorkin and Hermite-Besov spaces.”
SOBOLEV AND JAWERTH EMBEDDINGS FOR SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY (2009, methodology): “Following [ 18 ] and [19], these authors investigated the properties of the”
Coorbit spaces and wavelet coefficient decay over general dilation groups (2012, background): “But then we are left with the continuous wavelet transform with respect to scalar dilations, and the φ -transform characterization of [15] allows us to understand these spaces as coorbit spaces, either with respect to the irreducible representation arising from the similitude group, or with respect…”
Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, background): “Meyer’s wavelets [39] and the frames (the φ-transform) of Frazier and Jawerth [21, 22, 23] are the most striking examples of such decomposition systems playing a pivotal role in the solution of numerous theoretical and computational problems.”
Decomposition of weighted Triebel–Lizorkin and Besov spaces on the ball (2007, background): “Meyer’s wavelets [12] and the ’-transform of Frazier and Jawerth [ 6 , 7, 8] provide such building blocks for decomposition of Triebel-Lizorkin and Besov spaces in the classical case on Rd.”
Continuous wavelets on compact manifolds (2008, background): “(The analogous problems on R were solved in [12] and [13].”
Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis (2008, methodology): “As already mentioned, first results on atomic decompositions of that type go back to Frazier and Jawerth [14], [15], [16].”
Wavelet transforms for homogeneous mixed-norm Triebel–Lizorkin spaces (2016, methodology): “In our treatment of wavelets, we use the convenient approach of Frazier and Jawerth by adapting their φtransform from [12, 13], which to some extent bridges the gap between harmonic analysis and the general multiresolution analysis within wavelet theory.”