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\( H^{p}_{w} - L^{p}_{w} \) Boundedness of Marcinkiewicz Integral

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Abstract.

The Marcinkiewicz integral is essentially a Littlewood-Paley g-function, which plays a very important role in harmonic analysis. In this paper we give weaker smoothness conditions assumed on Ω to imply the \( H^{p}_{w} - L^{p}_{w} \) boundedness of the Marcinkiewicz integral operator μΩ, where w belongs to the Muckenhoupt weight class.

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  1. Department of Mathematics, National Central University, Chung-Li, Taiwan, 320, Republic of China

    Chin-Cheng Lin & Ying-Chieh Lin

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  1. Chin-Cheng Lin
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  2. Ying-Chieh Lin
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Correspondence to Chin-Cheng Lin.

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Lin, CC., Lin, YC. \( H^{p}_{w} - L^{p}_{w} \) Boundedness of Marcinkiewicz Integral. Integr. equ. oper. theory 58, 87–98 (2007). https://doi.org/10.1007/s00020-006-1475-8

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  • DOI: https://doi.org/10.1007/s00020-006-1475-8

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