A new weak type estimate for Marcinkiewicz integrals on weighted Hardy spaces

Details A new weak type estimate for Marcinkiewicz integrals on weighted Hardy spaces A new weak type estimate for Marcinkiewicz integrals on weighted Hardy spaces

2011-11-22

arxiv.org/abs/1111.5075v1

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

The Marcinkiewicz integral $\mu_\Omega$ is essentially a Littlewood-Paley $g$-function, which plays a important role in harmonic analysis. In this paper, by using the atomic decomposition theory of weighted Hardy spaces, we will obtain the weighted weak type estimate of $\mu_\Omega$ on these spaces, under some Dini type condition imposed on the kernel $\Omega$. This result is new even in the unweighted case.

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