Classical and modern Fourier analysis

By Loukas Grafakos. 2003

1,155 citations recorded by the source corpus.

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Citations in the corpus

Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations (2013, unknown): “, [14]) there exist C1 = C1(n,A, ν) and p1 = p1(n,A, ν) > 1 such that w(B0) w(Br(yi)) ≤ C1 [ |B0| |Br(yi)| ]p1 .”
Gaussian subordination for the Beurling-Selberg extremal problem (2010, background): “Our notation and terminology for distributions follows that of [7], and precise definitions for these spaces are given in [7, Section 2.”
Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces (2005, methodology): “Attention was paid to the constants in [Gr] but Buckley’s sharp estimate for ‖M‖Lp(w) was missing; with this additional information, the constants in [Gr] would be of the same order as the ones obtained here.”
Fourier multipliers of classical modulation spaces (2006, background): “Therefore each (Tjφ)f is a Fourier multiplier for L(R), p ∈ (1,∞), and in fact ∥∥(Tjφ)f ∥∥MF (Lp) Cd,p(A0 + ∥∥(Tjφ)f ∥∥∞) Cd,p(A0 + ‖φ‖∞‖f ‖∞), where Cd,p is a constant depending on p and the dimension d , see [13].”
Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators (2006, background): “The following facts are well known (see, for instance, [12,13]).”
Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights (2006, background): “We refer the reader to [40] and [39] for more details on this topic.”
New Abstract Hardy Spaces (2007, background): “We have the well-known following properties (chapter 9 of [25] for the Euclidean case) : Proposition 6.”
Summability of Multi-Dimensional Trigonometric Fourier Series (2012, methodology): “One of the deepest results in harmonic analysis is Carleson’s theorem, that the partial sums of the Fourier series converge almost everywhere to f ∈ Lp(T) (1 < p ≤ ∞) (see Carleson [18] and Hunt [51] or recently Grafakos [43]).”
Decay estimates for a class of wave equations (2008, background): “For their proof we refer the readers to [12], [5].”
Nonlinear Measure Data Problems (2011, background): “Useful references for Lorentz spaces are for instance [45, 88].”
Weighted little bmo and two-weight inequalities for Journé commutators (2017, background): “3 in [9]): For any 1 < p < ∞ and B > 1, there exist positive constants (2.”
Vector-valued singular integrals and maximal functions on spaces of homogeneous type (2009, background): “see, for example, [7] or [17] for more details.”
Linear Potentials in Nonlinear Potential Theory (2013, background): “For more on Lorentz spaces we for instance refer to [13].”