Vol. 14, No. 2, 2021

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

Volume 17
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

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.
Pointwise differentiability of higher-order for distributions

Ulrich Menne

Vol. 14 (2021), No. 2, 323–354
Abstract

For distributions, we build a theory of higher-order pointwise differentiability comprising, for order zero, Łojasiewicz’s notion of point value. Results include Borel regularity of differentials, higher-order rectifiability of the associated jets, a Rademacher–Stepanov-type differentiability theorem, and a Lusin-type approximation. A substantial part of this development is new also for zeroth order. Moreover, we establish a Poincaré inequality involving the natural norms of negative order of differentiability. As a corollary, we characterise pointwise differentiability in terms of point values of distributional partial derivatives.

PDF Access Denied

We have not been able to recognize your IP address 3.133.133.110 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
distribution, higher-order pointwise differentiability, \Lojasiewicz point value, asymptotic expansion, higher-order rectifiability, Rademacher–Stepanov-type theorem, Lusin-type approximation, Poincaré inequality
Mathematical Subject Classification
Primary: 46F10
Secondary: 26B05, 41A58
Milestones
Received: 28 March 2018
Revised: 17 August 2019
Accepted: 21 November 2019
Published: 20 March 2021
Authors
Ulrich Menne
Department of Mathematics
National Taiwan Normal University
Taipei City
Taiwan (R. O. C.)
Mathematical Division
National Center for Theoretical Sciences
Taipei City
Taiwan (R. O. C.)