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arXiv · 1702.03870

Weighted inequalities for product fractional integrals

Eric T. Sawyer·Zipeng Wang
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Abstract

We investigate one and two weight norm inequalities for product fractional integrals. We show that in the one weight case, most of the 1 parameter theory carries over to the 2 parameter setting. However, in the two weight case, apart from the trivial case of product weights, the rectangle characteristic never controls the operator norm without side conditions. The Stein-Weiss extension of the classical Hardy-Littlewood-Sobolev inequality carries over to the setting of 2 parameters with nonproduct power weights using a sandwiching technique.

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Eric T. Sawyer, Zipeng Wang. 2017-02-13. Weighted inequalities for product fractional integrals. https://arxiv.org/abs/1702.03870

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