Functional inequalities for time-changed symmetric \(\alpha \)-stable processes
type: Item
instance of: scholarly article
title: Functional inequalities for time-changed symmetric \(\alpha \)-stable processes
zbMATH Open document ID: 1477.60117
author: Jian Wang
author: Longteng Zhang
published in: Frontiers of Mathematics in China
publication date: 2021-08-05T00:00:00Z
review text: For \(\alpha\in (0, 2),\) let \(Z := (Z_t)_{t>0}\) be a (rotationally invariant) symmetric \(\alpha\)-stable process on \(\mathbb R^d,\) whose infinitesimal generator is given by the fractional Laplacian \(-(-\Delta)^{\alpha/2}.\) The authors consider time-changed symmetric \(\alpha\)-stable processes and establish sharp functional inequalities for such processes with \(d > 1\), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function \(W(x) = (1+|x|)^\beta\) with \(\beta > \alpha\), optimal Nash-type inequalities are obtained, which in turn give optimal upper bounds for the density function of the associated semigroups.
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 60J76
zbMATH DE Number: 7379093
zbMATH Keywords: symmetric \(\alpha \)-stable process
zbMATH Keywords: time change
zbMATH Keywords: functional inequality
reviewed by: Nasir N. Ganikhodjaev
MaRDI profile type: Publication
full work available at URL: s11464-021-0908-7
OpenAlex ID: W3138987571
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DOI: 10.1007/S11464-021-0908-7
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description: scientific article; zbMATH DE number 7379093