Weighted Estimates for Bilinear Fractional Integral Operators and their Commutators

In this paper, we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators; that is, we prove the weighted Lp norm of the operator is bounded by the weighted Lp norm of a n...

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Bibliographic Details
Published in:Indiana University mathematics journal 2018-01, Vol.67 (1), p.397-428
Main Authors: Hoang, Cong, Moen, Kabe
Format: Article
Language:English
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Summary:In this paper, we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators; that is, we prove the weighted Lp norm of the operator is bounded by the weighted Lp norm of a natural maximal operator when the weight belongs to A∞. As a corollary, we are able to obtain new weighted estimates for the bilinear maximal function associated with the bilinear Hubert transform. Finally, as an application of our results, we prove a bilinear Stein-Weiss inequality.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2018.67.6271