The intrinsic square function

By Michael Wilson. 2007

110 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/81f2967458cd7c14aa4b038ffcc82efe095ae77e

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In Applied Mathematics

Citations in the corpus

The sharp weighted bound for general Calderon-Zygmund operators (2010, methodology): “By a different method, Lerner [19] was able to estimate all standard convolution-type operators in arbitrary dimension by controlling them in terms of Wilson’s intrinsic square function [32]; however, this approach only gave (1.”
Intrinsic square functions on the weighted Morrey spaces (2011, background): “[26] M. Wilson, Weighted Littlewood-Paley Theory and Exponential-Square Integrability, Lecture Notes in Math, Vol 1924, Springer-Verlag, 2007.”
Borderline weak‐type estimates for singular integrals and square functions (2015, background): “Define the intrinsic square function of Wilson [23] Gα, for 0 α 1 by Gαf(x)2 = ∫ Γ(x) Aαf(y, t)2 dydt tn+1 , where Γ(x) := {(y, t) ∈ Rn+1+ : |y| t} is the cone of aperture one in the upper-half plane, and Aαf(x, t) = sup γ∈Cα |f ∗ γt(x)|, where γt(x) = t−nγ(xt−n) and Cα is the collection of fu”
A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions☆ (2009, methodology): “(iv) We finally remark that a continuous version of the grand Littlewood-Paley function ( ∑ k∈Z supφ∈A |φ2−k ∗ f | 2)1/2 with a different choice of A was used by Wilson [38] to solve a conjecture of R. Fefferman and E. M. Stein on the weighted boundedness of the classical Littlewood-Paley S-function”
On Sharp Aperture-Weighted Estimates for Square Functions (2013, background): “For non-compactly supported ψ some additional ideas from [19] can be used that lead to even worst estimate on γ(α).”
Sharp weighted norm inequalities for Littlewood-Paley operators and singular integrals (2010, background): “As it was shown in [23], the intrinsic square function pointwise dominates both classical square functions and their more recent analogs.”
The sharp weighted bound for general Calderón-Zygmund operators (2010, methodology): “ese operators. By a diﬀerent method, Lerner [16] was able to estimate all standard convolution-type operators in arbitrary dimension by controlling them in terms of Wilson’s intrinsic square function [26]; however, this approach only gave (1.2) for p ∈ (1, 3 2] ∪ [3,∞). (5) The conjecture(1.1) conce”
Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents (2014, methodology): “(ii) Recall that Liang and Yang [28] characterized the Musielak-Orlicz Hardy space H(R) in terms of the intrinsic square functions original introduced by Wilson [44].”