Abstract
Let T be the multilinear Calderon-Zygmund operator with non-smooth kernel and let T ∗ be its corresponding maximal operator. In this paper, vector-valued weighted norm inequalities for T and T ∗ are established. As applications, weighted strong type estimates for vector-valued commutators associated with T and T ∗ are deduced respectively.
Highlights
1 Introduction and main results Let T be a multilinear operator initially defined on the m-fold product of Schwartz spaces and taking values in the space of tempered distributions, T : S Rn × · · · × S Rn → S Rn
Qj < ∞, it extends to a bounded multilinear operator from Lq × · · · × Lqm to Lq, where
Competing interests The author declares that he has no competing interests
Summary
We have (i) There exists a constant C > such that l. Can be seen as the vector-valued extension of Theorem . In [ ] and Theorem C, respectively
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