Sharp weighted bounds involving A

By Tuomas Hytönen, C. P'erez. 2011

368 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/cdbf500247fe3dac6d97cb8b4be80cd5e88917cc

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

A Fractional Muckenhoupt–Wheeden Theorem and its Consequences (2013, background): “Following the work of Hytönen and Pérez [13], we find sharp constants in terms of [u, σ]Aαp,q , [u]AM∞ and [σ]AM∞ .”
The A_p-A_infty inequality for general Calderon--Zygmund operators (2011, background): “• The case p = 2 of the Theorem for untruncated operators, from [5]: ‖Tf‖L2(w) ≤ CT [w] 1/2 A2 ( [w] 1/2 A∞ + [w] 1/2 A∞ ) ‖f‖L2(w).”
On Sharp Aperture-Weighted Estimates for Square Functions (2013, methodology): “We will use the following proposition from [10].”
Extrapolation for multilinear compact operators and applications (2020, background): “Let us recall the sharp reverse Hölder’s inequality from [23, 41, 45].”
Weighted Norm Inequalities for Rough Singular Integral Operators (2017, methodology): “Another basic tool for us is the following classical reverse Hölder inequality with optimal bound, as obtained in [28] (see also [30]).”
Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, methodology): “A bit later this result was improved in [12] in the case p = 2 and for general p in [10].”
A Simple Proof of the A2 Conjecture (2013, methodology): “We will use the one from [11].”
Sharp Bekolle estimates for the Bergman projection (2012, background): “l Bergman projection. Let us consider the following system of dyadic grids Dβ := {2j([0,1)+m+(−1)jβ) : m ∈ Z,j ∈ Z} for β ∈ {0,1/3}. These systems have been recently considered by Hyto¨nen and P´erez [17], Lerner [20] and Lacey, Hyto¨nen and P´erez [16] in their simpliﬁed versions of the A 2 Theorem”
Representation of singular integrals by dyadic operators, and the A_2 theorem (2011, background): “It is also possible to apply a version of the extrapolation argument to the mixed A2/A∞ bounds [9], but this did not give the optimal results for p 6= 2.”
One and two weight norm inequalities for Riesz potentials (2012, background): “ Z Q M(χQw)(x)dx < ∞, where M is the Hardy-Littlewood maximal operator. Independently, Fujii [8] and Wilson [41, 42] (also see [43]) showed that w ∈ A∞ if and only if w ∈ A′ ∞. P´erez and Hyto¨nen [15] showed that [w]A′ ∞ . [w]A , and in fact [w]A′ ∞ can be substantially smaller. Using this deﬁni”
Sarason Conjecture on the Bergman space (2013, methodology): “ over Carleson cubes. This deﬁnition of B∞ is motivated by the Muckenhoupt version A∞ described by Wilson in [46–48]. This A∞ deﬁnition appears in the recent works of Lerner [28], Hyto¨nen and P´erez [21] and Hyto¨nen and Lacey [20] among others, where it is used to ﬁnd sharp estimates in terms of t”
On an estimate of Calderón-Zygmund operators by dyadic positive operators (2012, methodology): “8) was deduced in [12] from a sharp version of the reverse Hölder inequality, along with the estimate (2.”