Growth Envelopes of Anisotropic Function Spaces

Abstract

The present paper is devoted to the study of growth envelopes of anisotropic function spaces. An affirmative answer is given to the question of H. Triebel [Wavelet bases in anisotropic function spaces. In: 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.