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

Frank, Rupert L. and Ivanisvili, Paata (2021) Hypercontractivity of the semigroup of the fractional Laplacian on the n-sphere. Journal of Functional Analysis, 281 (8). Art. No. 109145. ISSN 0022-1236. https://resolver.caltech.edu/CaltechAUTHORS:20210628-191053213

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jfa.2021.109145DOIArticle
https://arxiv.org/abs/2101.06209arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
NSFDMS-1954995
NSFDMS-2052645
NSFDMS-1856486
NSFDMS-2052865
NSFDMS-1945102
Subject Keywords:hypercontractivity; Poisson semigroup; n-Sphere
Issue or Number:8
Classification Code:MSC: 39B62; 42B35; 47A30
Record Number:CaltechAUTHORS:20210628-191053213
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210628-191053213
Official Citation:Rupert L. Frank, Paata Ivanisvili, Hypercontractivity of the semigroup of the fractional Laplacian on the n-sphere, Journal of Functional Analysis, Volume 281, Issue 8, 2021, 109145, ISSN 0022-1236, https://doi.org/10.1016/j.jfa.2021.109145.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109624
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:29 Jun 2021 14:43
Last Modified:29 Jun 2021 14:43

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