Hypercontractivity of the semigroup of the fractional Laplacianon the n-sphere

Frank, Rupert L. and Ivanisvili, Paata (2021): Hypercontractivity of the semigroup of the fractional Laplacianon the n-sphere. In: Journal of Functional Analysis, Vol. 281, No. 8, 109145

Abstract

For 1 < p <= q we show that the Poisson semigroup e(-t root-Delta) on the n-sphere is hypercontractive from L-p to L-q in dimensions n <= 3 if and only if e(-t root n) <= root p-1/q-1. We also show that the equivalence fails in large dimensions. (C) 2021 Elsevier Inc. All rights reserved.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-1236
• Language: English