Mathematische Zeitschrift

, Volume 259, Issue 1, pp 131–169

Duality and interpolation of anisotropic Triebel–Lizorkin spaces

Article

DOI: 10.1007/s00209-007-0216-2

Cite this article as:
Bownik, M. Math. Z. (2008) 259: 131. doi:10.1007/s00209-007-0216-2

Abstract

We study properties of anisotropic Triebel–Lizorkin spaces associated with general expansive dilations and doubling measures on \({\mathbb{R}}^n\) using wavelet transforms. This paper is a continuation of (Bownik in J Geom Anal 2007, to appear, Trans Am Math Soc 358:1469–1510, 2006), where we generalized the isotropic methods of dyadic \(\varphi\) -transforms of Frazier and Jawerth (J Funct Anal 93:34–170, 1990) to non-isotropic settings. By working at the level of sequence spaces, we identify the duals of anisotropic Triebel–Lizorkin spaces. We also obtain several real and complex interpolation results for these spaces.

Keywords

Anisotropic Triebel–Lizorkin spaceExpansive dilationDoubling measure\(\varphi\) -transformWavelet transformDual spaceReal interpolationComplex interpolation

Mathematics Subject Classification (2000)

Primary 42B2542B3542C40Secondary 46B7047B3747B38

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OregonEugeneUSA