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Published October 15, 2021 | Submitted
Journal Article Open

Hypercontractivity of the semigroup of the fractional Laplacian on the n-sphere

Abstract

For 1 < p ≤ q we show that the Poisson semigroup e^(-t√-Δ) on the n-sphere is hypercontractive from L^p to L^q in dimensions n ≤ 3 if and only if e^(-t√n) ≤ √((p - 1)/(q - 1)). We also show that the equivalence fails in large dimensions.

Additional Information

© 2021 Elsevier. Received 17 January 2021, Accepted 14 June 2021, Available online 18 June 2021. Partial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) as well as DMS-2052645, DMS-1856486, and CAREER-DMS-2052865, CAREER-DMS-1945102 (P.I.) is acknowledged.

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Created:
August 22, 2023
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October 23, 2023