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Zeitschrift für Analysis und ihre Anwendungen


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Volume 32, Issue 3, 2013, pp. 257–277
DOI: 10.4171/ZAA/1484

Published online: 2013-07-03

Characterisation by Local Means of Anisotropic Lizorkin-Triebel Spaces with Mixed Norms

J. Johnsen[1], S. Munch Hansen[2] and Winfried Sickel[3]

(1) Aalborg Universitet, Denmark
(2) Aalborg Universitet, Denmark
(3) Friedrich-Schiller-Universität Jena, Germany

This is a contribution to the theory of Lizorkin-Triebel spaces having mixed Lebesgue norms and quasi-homogeneous smoothness. We discuss their characterisation in terms of general quasi-norms based on convolutions. In particular, this covers the case of local means, in Triebel's terminology. The main step is an extension of some crucial inequalities due to Rychkov to the case with mixed norms.

Keywords: Local means, mixed norms, moment conditions, Tauberian conditions

Johnsen J., Munch Hansen S., Sickel Winfried: Characterisation by Local Means of Anisotropic Lizorkin-Triebel Spaces with Mixed Norms. Z. Anal. Anwend. 32 (2013), 257-277. doi: 10.4171/ZAA/1484