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Weighted estimates for bilinear fractional integral operators: a necessary and sufficient condition for power weights

  • Yasuo Komori-FuruyaEmail author
Article
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Abstract

We consider weighted estimates for two bilinear fractional integral operators \(I_{2,\alpha }\) and \(BI_{\alpha }\). Moen (Collect Math 60:213–238, 2009) obtained a necessary and sufficient condition for \(I_{2,\alpha }\). However we know only some sufficient conditions for \(BI_{\alpha }\) which is a variant of the bilinear Hilbert transform. Restricted to power weights we obtain a necessary and sufficient condition for \(BI_{\alpha }\). We also prove a bilinear Stein–Weiss inequality.

Keywords

Bilinear fractional integral operator Weight Stein–Weiss inequality 

Mathematics Subject Classification

42B20 

Notes

Acknowledgements

The author would like to thank the referee for his/her helpful suggestions.

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Copyright information

© Universitat de Barcelona 2019

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceTokai UniversityHiratsukaJapan

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