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 | ||||||||||||||
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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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Subject Keywords: | hypercontractivity; Poisson semigroup; n-Sphere | ||||||||||||||
Issue or Number: | 8 | ||||||||||||||
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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