Weak type estimates of Marcinkiewicz integrals on the weighted Hardy spaces and weighted Herz-type Hardy spaces

Details Weak type estimates of Marcinkiewicz integrals on the weighted Hardy spaces and weighted Herz-type Hardy spaces Weak type estimates of Marcinkiewicz integrals on the weighted Hardy spaces and weighted Herz-type Hardy spaces

2010-12-03

arxiv.org/abs/1012.0654v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

The Marcinkiewicz integral is essentially a Littlewood-Paley $g$-function,
which plays a important role in harmonic analysis. In this article, by using
the atomic decomposition theory of weighted Hardy spaces and homogeneous
weighted Herz-type Hardy spaces, we will obtain some weighted weak type
estimates for Marcinkiewicz integrals on these spaces.

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