A+ CATEGORY SCIENTIFIC UNIT

Vector-valued wavelets and the Hardy space $H^1({\Bbb R}^n,X)$

Volume 172 / 2006

Tuomas Hytönen Studia Mathematica 172 (2006), 125-147 MSC: 42B30, 42C40, 46E40. DOI: 10.4064/sm172-2-2

Abstract

We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space $H^1(\Bbb R^n)$ for the space $H^1(\Bbb R^n,X)$ of $X$-valued functions. Here $X$ is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón–Zygmund operators on Bochner spaces and some new local estimates.

Authors

  • Tuomas HytönenDepartment of Mathematics
    University of Turku
    FI-20014 Turku, Finland
    e-mail

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