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. doi:10.1016/j.jfa.2021.109145. 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:

URL	URL Type	Description
https://doi.org/10.1016/j.jfa.2021.109145	DOI	Article
https://arxiv.org/abs/2101.06209	arXiv	Discussion Paper

ORCID:

Author	ORCID
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 Agency	Grant Number
NSF	DMS-1363432
NSF	DMS-1954995
NSF	DMS-2052645
NSF	DMS-1856486
NSF	DMS-2052865
NSF	DMS-1945102

Subject Keywords:

hypercontractivity; Poisson semigroup; n-Sphere

Issue or Number:

Classification Code:

MSC: 39B62; 42B35; 47A30

DOI:

10.1016/j.jfa.2021.109145

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:

16 Nov 2021 19:37

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