Marcinkiewicz integral on weighted Hardy spaces

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Abstract

In this paper we give sufficient conditions to imply the Hw 1-Lw1 boundedness, of the Marcinkiewicz integral operator μω, where w is a Muckenhoupt weight. We also prove that, under the stronger condition ω ∈ Lip α, the operator μω is bounded from H wp to Lwp for max{n/(n + 1/2), n/(n + α)} < p < 1.

Original languageEnglish
Pages (from-to)620-629
Number of pages10
JournalArchiv der Mathematik
Volume80
Issue number6
DOIs
StatePublished - 1 Jun 2003

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