Taiwanese Journal of Mathematics

WEAK HARDY SPACES $H^{p,\infty}$ ON SPACES OF HOMOGENEOUS TYPE AND THEIR APPLICATIONS

Xinfeng Wu and Xiaohua Wu

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Abstract

In this paper, we introduce weak Hardy spaces $H^{p,\infty}$ on spaces of homogeneous type. We establish an atomic decomposition characterization of these spaces, show the boundedness of fractional integral operators and provide an $H^{p,\infty}$ interpolation theorem. Applications to the Nagel-Stein's singular integral operators and fractional integral operators are also discussed.

Article information

Source
Taiwanese J. Math., Volume 16, Number 6 (2012), 2239-2258.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406849

Digital Object Identifier
doi:10.11650/twjm/1500406849

Mathematical Reviews number (MathSciNet)
MR3001845

Zentralblatt MATH identifier
1260.42015

Subjects
Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Keywords
weak Hardy spaces maximal functions singular integral space of homogeneous type

Citation

Wu, Xinfeng; Wu, Xiaohua. WEAK HARDY SPACES $H^{p,\infty}$ ON SPACES OF HOMOGENEOUS TYPE AND THEIR APPLICATIONS. Taiwanese J. Math. 16 (2012), no. 6, 2239--2258. doi:10.11650/twjm/1500406849. https://projecteuclid.org/euclid.twjm/1500406849


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