Document Type

Article

Publication Date

2013

Keywords

Sobolev inequality, Bessel potential, Riesz potential, Maximal function

Abstract

We revisit the Sobolev inequality for periodic functions on the d-dimensional torus. We provide an elementary Fourier analytic proof of this inequality which highlights both the similarities and differences between the periodic setting and the classical d-dimensional Euclidean one.

Publication Title

Publicationes Mathematicae Debrecen

Volume

83

Issue

3

First Page

359

Last Page

374

Required Publisher's Statement

Published by the Institute of Mathematics, University of Debrecen, Hungary.

Comments

This version is the author's post print.

Subjects - Topical (LCSH)

Sobolev spaces; Fourier series; Bessel polynomials; Torus (Geometry)

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

Included in

Mathematics Commons

Share

COinS