Mathematical Research Letters

Volume 19 (2012)

Number 1

Multilinear embedding estimates for the fractional Laplacian

Pages: 175 – 189

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n1.a14

Author

William Beckner (Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, USA)

Abstract

Three novel multilinear embedding estimates for the fractional Laplacian areobtained in terms of trace integrals restricted to the diagonal.The resulting sharp inequalities may be viewed as extensions of theHardy–Littlewood–Sobolev inequality, the Gagliardo–Nirenberginequality and Pitt’s inequality.

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