Published October 15, 2021
| Submitted
Journal Article
Open
Hypercontractivity of the semigroup of the fractional Laplacian on the n-sphere
- Creators
-
Frank, Rupert L.
- Ivanisvili, Paata
Chicago
An error occurred while generating the citation.
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.Attached Files
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Additional details
- Eprint ID
- 109624
- DOI
- 10.1016/j.jfa.2021.109145
- Resolver ID
- CaltechAUTHORS:20210628-191053213
- NSF
- DMS-1363432
- NSF
- DMS-1954995
- NSF
- DMS-2052645
- NSF
- DMS-1856486
- NSF
- DMS-2052865
- NSF
- DMS-1945102
- Created
-
2021-06-29Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field