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The commutators of multilinear Calderón–Zygmund operators on weighted Hardy spaces
Published online by Cambridge University Press: 26 June 2023
Abstract
In this paper, we study the behaviours of the commutators $[\vec b,\,T]$
generated by multilinear Calderón–Zygmund operators $T$
with $\vec b=(b_1,\,\ldots,\,b_m)\in L_{\rm loc}(\mathbb {R}^n)$
on weighted Hardy spaces. We show that for some $p_i\in (0,\,1]$
with $1/p=1/p_1+\cdots +1/p_m$
, $\omega \in A_\infty$
and $b_i\in \mathcal {BMO}_{\omega,p_i}$
($1\le i\le m$
), which are a class of non-trivial subspaces of ${\rm BMO}$
, the commutators $[\vec b,\,T]$
are bounded from $H^{p_1}(\omega )\times \cdots \times H^{p_m}(\omega )$
to $L^p(\omega )$
. Meanwhile, we also establish the corresponding results for a class of maximal truncated multilinear commutators $T_{\vec b}^*$
.
- Type
- Research Article
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- Copyright
- Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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