On Muckenhoupt–Wheeden Conjecture☆

By M. Reguera. 2010

60 citations recorded by the source corpus.

Abstract Let M denote the dyadic Maximal Function. We show that there is a weight w, and Haar multiplier T for which the following weak-type inequality fails sup t > 0 t w ( { x ∈ R : | T f ( x ) | > t } ) ⩽ C ∫ R | f | M w ( x ) d x . (With T replaced by M, this is a well-known fact.) This shows that a dyadic version of the so-called Muckenhoupt–Wheeden Conjecture is false. This accomplished by using current techniques in weighted inequalities to show that a particular L 2 consequence of the inequality above does not hold.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/93c52aa135032e9f45df7441516b136d05739215

How researchers see this paper

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In Applied Mathematics

1. G. Rey
2. C. Domingo-Salazar
3. Michael T. Lacey
4. Tuomas Hytönen
5. Kangwei Li
6. Andrei K. Lerner
7. D. Cruz-Uribe
8. C. Thiele

In Numerical Analysis

1. C. Domingo-Salazar
2. G. Rey
3. Michael T. Lacey

Citations in the corpus

• Borderline weak‐type estimates for singular integrals and square functions (2015, background): “But, the main counterexamples have at their heart a counterexample to an L2 inequality for martingale transforms, as in Reguera’s first paper on the subject [18].”