, Volume 259, Issue 1, pp 131-169

Duality and interpolation of anisotropic Triebel–Lizorkin spaces

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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.

The author was partially supported by the NSF grants DMS-0441817 and DMS-0653881. The author wishes to thank Michael Frazier and Dachun Yang for valuable comments and discussions on this work.