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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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Online
ISSN
1572-9176
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Volume 18, Issue 3 (Jan 2011)

Issues

Trace operators on fractals, entropy and approximation numbers

Cornelia Schneider
Published Online: 2011-07-14 | DOI: https://doi.org/10.1515/gmj.2011.0030

Abstract

First we compute the trace space of Besov spaces – characterized via atomic decompositions – on fractals Γ, for parameters 0 < p < ∞, 0 < q ≤ min(1, p) and s = (nd)/p. New Besov spaces on fractals are defined via traces for 0 < p, q ≤ ∞, s ≥ (nd)/p and some embedding assertions are established. We conclude by studying the compactness of the trace operator TrΓ by giving sharp estimates for entropy and approximation numbers of compact embeddings between Besov spaces. Our results on Besov spaces remain valid considering the classical spaces defined via differences. The trace results are used to study traces in Triebel–Lizorkin spaces as well.

Keywords.: Besov spaces; Triebel–Lizorkin spaces; d-sets; traces; entropy numbers; approximation numbers

About the article

Received: 2010-10-01

Published Online: 2011-07-14

Published in Print: 2011-09-01


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj.2011.0030.

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