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An integral representation formula for logarithmic potentials and embeddings of Bessel-potential spaces

Published online by Cambridge University Press:  26 May 2009

Shinya Moritoh  and
Yumi Tanaka
Shinya Moritoh
Affiliation:
Department of Mathematics, Nara Women's University, Nara 630-8506, Japan (moritoh@cc.nara-wu.ac.jp)
Yumi Tanaka
Affiliation:
Konoe-cho 160-205, Kamigyo-ku, Kyoto 602-8046, Japan
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Abstract

We give an integral representation formula for logarithmic Riesz potentials. This plays an essential role in proving the sharpness of the embeddings of Bessel-potential spaces, which have logarithmic exponents both in the smoothness and in the underlying Lorentz—Zygmund spaces. These results are natural extensions of those obtained by Edmunds, Gurka, Opic and Trebels.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 3 , June 2009 , pp. 541 - 549
Copyright
Copyright © Royal Society of Edinburgh 2009

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