Sharp A1 Bounds for Calderón-Zygmund Operators and the Relationship with a Problem of Muckenhoupt and Wheeden

By Andrei K. Lerner, S. Ombrosi, C. P'erez. 2008

90 citations recorded by the source corpus.

For any Calderon-Zygmund operator T the following sharp estimate is obtained for 1 < p < ∞:where . In the case where p = 2 and T is a classical convolution singular integral, this result is due to R. Fefferman and J. Pipher [7]. Then, we deduce the following weak type (1, 1) estimate related to a problem of Muckenhoupt and Wheeden [11]:where w ∈ A 1 and φ(t) = t(1 + log + t)(1 + log + log + t).

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/447c8e25134b53b417eaab3d1f46d0bfa906f6fc

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In Applied Mathematics

Citations in the corpus

A pointwise estimate for the local sharp maximal function with applications to singular integrals (2010, methodology): “7, as in [18], we use the following well-known results from [5, 8].”
A1 bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden (2009, background): “In a recent paper [8], the following results towards (1.”
Two weight norm inequalities for fractional integral operators and commutators (2014, background): “The weak (1, 1) conjecture appeared shortly before this in [61].”
Weighted Norm Inequalities for Rough Singular Integral Operators (2017, methodology): “We follow ideas from [35, 36, 28] combined with the pointwise estimate in Theorem 2.”
Extrapolation for multilinear compact operators and applications (2020, background): “1) Let us recall the sharp reverse Hölder’s inequality from [24, 44, 48].”
SHARP BOUNDS FOR GENERAL COMMUTATORS ON WEIGHTED LEBESGUE SPACES (2010, result): “Recently all the above results have been recovered using different sets of techniques and obtaining linear bounds for the larger class of Haar shift operators [20], [8].”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, result): “The next theorem is an analogy of the result due to Lerner, Ombrosi and Pérez [106].”
Borderline weak‐type estimates for singular integrals and square functions (2015, background): “Most of the prior arguments [8, 9, 14, 17] depend upon extrapolation-type arguments, namely establishing a range of L inequalities, and then making an appropriate choice of p ≈ 1 to conclude the argument at L(1).”