JournalszaaVol. 22 , No. 2DOI 10.4171/zaa/1151

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

  • M. Bricchi

    Università di Pavia, Italy
  • Susana D. Moura

    Universidade de Coimbra, Portugal
Complements on Growth Envelopes of Spaces with Generalized Smoothness in the Sub-Critical Case cover

Abstract

We describe the growth envelope of Besov and Triebel-Lizorkin spaces Bp,qσ(Rn)B_{p,q}^\sigma (\mathbb R^n) and Fp,qσ(Rn)F_{p,q}^\sigma (\mathbb R^n) with generalized smoothness, i.e.\ instead of the usual scalar regularity index σR\sigma \in \mathbb R we consider now the more general case of a sequence σ={σj}jN0\sigma = \{\sigma_j\}_{j \in\mathbb N_0}. We take under consideration the range of the parameters σ,p,q\sigma, p,q which, in analogy to the classical terminology, we call sub-critical.