Vol. 10, No. 4, 2017

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

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

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
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 52.23.219.12 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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