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Zeitschrift für Analysis und ihre Anwendungen

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Volume 27, Issue 1, 2008, pp. 95–118
DOI: 10.4171/ZAA/1346

Published online: 2008-03-31

Growth Envelopes of Anisotropic Function Spaces

Susana D. Moura[1], Júlio S. Neves[2] and Mariusz Piotrowski[3]

(1) Universidade de Coimbra, Portugal
(2) Universidade de Coimbra, Portugal
(3) Universität Wien, Austria

The present paper is devoted to the study of growth envelopes of aniso\-tro\-pic function spaces. An affirmative answer is given to the question of H.~Triebel [Wavelet bases in anisotropic function spaces. In: {\em Function Spaces, Differential Operators and Nonlinear Analysis} (FSDONA-04). Praha: Math. Inst. Acad. Czech Rep. 2005, pp.~370 -- 387; Conjecture~13], whether the growth envelopes are independent of anisotropy. As an application, related anisotropic Hardy inequalities are presented and we also discuss a connection to some anisotropic fractal sets.

Keywords: Anisotropic function spaces, growth envelopes, Hardy inequalities

Moura Susana, Neves Júlio, Piotrowski Mariusz: Growth Envelopes of Anisotropic Function Spaces. Z. Anal. Anwend. 27 (2008), 95-118. doi: 10.4171/ZAA/1346