Article
The Sobolev Inequality on the Torus Revisited
Publicationes Mathematicae Debrecen
Document Type
Article
Publication Date
1-1-2013
Keywords
- Sobolev inequality,
- Bessel potential,
- Riesz potential,
- Maximal function
Disciplines
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.
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
Citation Information
Árpád Bényi and Tadahiro Oh. "The Sobolev Inequality on the Torus Revisited" Publicationes Mathematicae Debrecen Vol. 83 Iss. 3 (2013) p. 359 - 374 Available at: http://works.bepress.com/arpad_benyi/9/
This version is the author's post print.