Modern Fourier Analysis

By Loukas Grafakos. 2008

1,558 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ffa6c39a1847ee2e2b42a520e560edb7cb0155d0

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In Theoretical Computer Science

Citations in the corpus

Variable Hardy Spaces (2012, background): “The classical theory of Hp spaces, 0 < p ≤ 1, is well known (see [12, 14, 15, 22, 26]), and our goal is to replicate that theory as much as possible in this more general setting.”
A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions☆ (2009, neutral): “Recall that Ṁ1, p(Rn) = Ḟ 1 p, 2(R n) when p ∈ (n/(n + 1), ∞) by [30], AḞ 0 p,∞(R n) = Lp(Rn) when p ∈ (1, ∞) and AḞ 0 p,∞(R n) = Hp(Rn) when p ∈ (n/(n + 1), 1], where A = A−1, m with l ≥ 1 and m ∈ (n+ 1, ∞), and H p(Rn) is the classical real Hardy space (see [33, 16]).”
A Thought on Generalized Morrey Spaces (2018, background): “For the properties of these commutators we refer to [26].”
Localized Hardy Spaces $H^1$ Related to Admissible Functions on RD-Spaces and Applications to Schr\ (2009, background): “1 Introduction The theory of Hardy spaces on the Euclidean space Rn plays an important role in various fields of analysis and partial differential equations; see, for examples, [48, 18, 5, 47, 20].”
Rough Bilinear Singular Integrals (2015, background): “Then recall the lemma from Appendix B1 of [14], by defining Ψ(x) = 1 (1+|x|)2n+1 we have that for t ∈ [0,1] (|Ki| ∗Ψi− j)(x− ty)”
New real-variable characterizations of Musielak-Orlicz Hardy spaces (2012, methodology): “We have the following properties for Aq(R n) with q ∈ [1,∞), whose proofs are similar to those in [15, 16].”
Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, background): “1 Introduction The real-variable theory of Hardy spaces on the Euclidean space R certainly plays an important role in analysis, including harmonic analysis, partial differential equations and geometrical analysis, and has been systematically studied and developed so far; see, for example, [26, 32, 5”