Local growth envelopes of spaces of generalized smoothness: the subcritical case

Abstract

The concept of local growth envelope (ℰLGA, u) of the quasi-normed function space A is applied to the spaces of generalized smoothness B(s,ψ) pq (ℝn) and F(s,ψ)pq (ℝn) and it is shown that the influence of the function ψ, which is a fine tuning of the main smoothness parameter s, is strong enough in order to show up in the corresponding growth envelopes.