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Multilinear embedding estimates for the fractional Laplacian. (English) Zbl 1291.35426

Summary: Three novel multilinear embedding estimates for the fractional Laplacian are obtained in terms of trace integrals restricted to the diagonal. The resulting sharp inequalities may be viewed as extensions of the Hardy-Littlewood-Sobolev inequality, the Gagliardo-Nirenbergin equality and Pitt’s inequality.

MSC:

35R11 Fractional partial differential equations
35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
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