Growth Envelopes of Anisotropic Function Spaces

  • Susana D. Moura

    Universidade de Coimbra, Portugal
  • Júlio S. Neves

    Universidade de Coimbra, Portugal
  • Mariusz Piotrowski

    Universität Wien, Austria


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.

Cite this article

Susana D. Moura, Júlio S. Neves, Mariusz Piotrowski, Growth Envelopes of Anisotropic Function Spaces. Z. Anal. Anwend. 27 (2008), no. 1, pp. 95–118

DOI 10.4171/ZAA/1346