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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, 97403–1222, USA

    Marcin Bownik

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  1. Marcin Bownik
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Correspondence to Marcin Bownik.

Additional information

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.

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Bownik, M. Duality and interpolation of anisotropic Triebel–Lizorkin spaces. Math. Z. 259, 131–169 (2008). https://doi.org/10.1007/s00209-007-0216-2

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  • DOI: https://doi.org/10.1007/s00209-007-0216-2

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