Littlewood-Paley Theory and the Study of Function Spaces

By Michael Frazier, B. Jawerth, Guido L. Weiss. 1991

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Citations in the corpus

Convergence guarantees for kernel-based quadrature rules in misspecified settings (2016, background): “Lemma 1 is a variant of Lemma (1.1) of [12], from which we borrowed the proof idea.”
Group Invariant Scattering (2011, background): “As opposed to wavelet bases, a Littlewood-Paley wavelet transform [7, 14] is a redundant representation that computes convolution values at all x 2 R without subsampling: (2.”
The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations (2000, methodology): “20 in [22], the continuous versions of the spaces introduced above are actually isomorphic to their respective discrete versions via an wavelet transform.”
Scattered-Data Interpolation on Rn: Error Estimates for Radial Basis and Band-Limited Functions (2004, methodology): “The approach we take is based on the Calderón decomposition formula [5, 10], which essentially states that if f ∈ L(2)(R), then”
Weighted anisotropic product Hardy spaces and boundedness of sublinear operators (2009, background): “1, we need the following auxiliary lemma, which generalizes Lemma 2 and Lemma 4 in Appendix (III) of [28].”
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.”
New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities (2004, background): “The SDD is a principle for localizing objects in the frequency plane that goes beyond classical Littlewood-Paley theory [25].”
ATOMIC DECOMPOSITION OF HARDY-MORREY SPACES WITH VARIABLE EXPONENTS (2015, background): “For simplicity, we refer the reader to [20, 21] for the definitions of the φ-ψ transform and smooth N -atom, N ∈ N.”
Localized Tight Frames on Spheres (2006, unknown): “They provide a redundancy that helps reduce the effect of noise in data, and they have been constructed, studied, and employed extensively in both theoretical and applied problems [1, 2, 6, 7, 10, 12].”