Vol. 10, No. 4, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Improving Beckner's bound via Hermite functions

Paata Ivanisvili and Alexander Volberg

Vol. 10 (2017), No. 4, 929–942
Abstract

We obtain an improvement of the Beckner inequality f22 fp2 (2 p)f22 valid for p [1,2] and the Gaussian measure. Our improvement is essential for the intermediate case p (1,2), and moreover, we find the natural extension of the inequality for any real p.

Keywords
Poincaré inequality, log-Sobolev inequality, Sobolev inequality, Beckner inequality, Gaussian measure, log-concave measures, semigroups, Hermite polynomials, Hermite differential equation, confluent hypergeometric functions, Turán's inequality, error term in Jensen's inequality, phi-entropy, phi-Sobolev, F-Sobolev, phi-divergence, information theory, backwards heat, Monge–Amperè with drift, exterior differential systems
Mathematical Subject Classification 2010
Primary: 42B37, 52A40, 35K55, 42C05, 60G15
Secondary: 33C15, 46G12
Milestones
Received: 28 June 2016
Revised: 30 January 2017
Accepted: 18 March 2017
Published: 9 May 2017
Authors
Paata Ivanisvili
Department of Mathematics
Kent State University
Kent, OH 44240
United States
Alexander Volberg
Department of Mathematics
Michigan State University
East Lansing, MI 48824
United States