Local growth envelopes of spaces of generalized smoothness: the subcriticalcase

Abstract

The concept of local growth envelope (εLGA, u) of the quasi-normed function space A is applied to the spaces of generalized smoothness B(s,psi) pq (Rn) and F(s,psi)pq (Rn) and it is shown that the influence of the function psi, which is a fine tuning of the main smoothness parameter s, is strong enough in order to show up in the corresponding growth envelopes. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)