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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 2, 2003, pp. 383–398
DOI: 10.4171/ZAA/1151

Published online: 2003-06-30

Complements on Growth Envelopes of Spaces with Generalized Smoothness in the Sub-Critical Case

M. Bricchi[1] and Susana D. Moura[2]

(1) Università di Pavia, Italy
(2) Universidade de Coimbra, Portugal

We describe the growth envelope of Besov and Triebel-Lizorkin spaces $B_{p,q}^\sigma (\mathbb R^n)$ and $F_{p,q}^\sigma (\mathbb R^n)$ with generalized smoothness, i.e.\ instead of the usual scalar regularity index $\sigma \in \mathbb R$ we consider now the more general case of a sequence $\sigma = \{\sigma_j\}_{j \in\mathbb N_0}$. We take under consideration the range of the parameters $\sigma, p,q$ which, in analogy to the classical terminology, we call sub-critical.

Keywords: Besov spaces, generalized smoothness, growth-envelope functions

Bricchi M., Moura Susana: Complements on Growth Envelopes of Spaces with Generalized Smoothness in the Sub-Critical Case. Z. Anal. Anwend. 22 (2003), 383-398. doi: 10.4171/ZAA/1151