Product of functions in $\BMO$ and $\H^{1}$ in non-homogeneous spaces

Details Product of functions in $\BMO$ and $\H^{1}$ in non-homogeneous spaces Product of functions in $\BMO$ and $\H^{1}$ in non-homogeneous spaces

2009-06-27

arxiv.org/abs/0906.5095v2

Mathematics

Classical Analysis and ODEs

15 pages, I have added a lemma to prove that the product of a function in RBMO with a test function belongs to RBMO, accepted

Scientific paper

Under the assumption that the underlying measure is a non-negative Radon
measure which only satisfies some growth condition and may not be doubling, we
define the product of functions in the regular $BMO$ and the atomic block
$\H^{1}$ in the sense of distribution, and show that this product may be split
into two parts, one in $L^{1}$ and the other in some Hardy-Orlicz space.

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