New weighted estimates for bilinear fractional integral operators
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Abstract:
We prove a plethora of weighted estimates for bilinear fractional integral operators of the form \[ BI_\alpha (f,g)(x)=\int _{\mathbb {R}^n}\frac {f(x-t)g(x+t)}{|t|^{n-\alpha }} dt, \qquad 0<\alpha <n.\] When the target space has an exponent greater than one, many weighted estimates follow trivially from Hölder’s inequality and the known linear theory. We address the case where the target Lebesgue space is at most one and prove several interesting one and two weight estimates. As an application we formulate a bilinear version of the Stein-Weiss inequality for fractional integrals.References
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Additional Information
- Kabe Moen
- Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350
- Received by editor(s): November 7, 2011
- Published electronically: July 26, 2013
- Additional Notes: The author was partially supported by NSF Grant 1201504
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 627-646
- MSC (2010): Primary 42B20, 26A33
- DOI: https://doi.org/10.1090/S0002-9947-2013-06067-9
- MathSciNet review: 3130311