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arXiv · 1303.3424

A fractional Muckenhoupt-Wheeden theorem and its consequences

David Cruz-Uribe·Kabe Moen
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Abstract

In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of the $A_2$ conjecture we prove a related pair of conjectures linking the Riesz potential and the fractional maximal operator. As a consequence we are able to prove a number of sharp one and two weight norm inequalities for the Riesz potential.

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BibTeXRIS

David Cruz-Uribe, Kabe Moen. 2013-04-11. A fractional Muckenhoupt-Wheeden theorem and its consequences. https://arxiv.org/abs/1303.3424

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