Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers
By The Anh Bui, Xuan Thinh Duong. 2011
47 citations recorded by the source corpus.
Let $T$ be a multilinear operator which is bounded on certain products of unweighted Lebesgue spaces of $\mathbb R^n$. We assume that the associated kernel of $T$ satisfies some mild regularity condition which is weaker than the usual H\"older continuity of those in the class of multilinear Calder\'on-Zygmund singular integral operators. We then show the boundedness for $T$ and the boundedness of the commutator of $T$ with BMO functions on products of weighted Lebesgue spaces of $\mathbb R^n$. As an application, we obtain the weighted norm inequalities of multilinear Fourier multipliers and of their commutators with BMO functions on the products of weighted Lebesgue spaces when the number of derivatives of the symbols is the same as the best known result for the multilinear Fourier multipliers to be bounded on the products of unweighted Lebesgue spaces.
Subfields: Applied Mathematics, Gender Studies, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e85dcfea7f0adfc133a6660c6c5012d54d324514
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In Applied Mathematics
In Gender Studies
In Mathematical Physics
Citations in the corpus
- Sparse Domination Theorem for Multilinear Singular Integral Operators with $L^{r}$-Hörmander Condition (2016, background): “it is shown in [2] that multilinear Mihlin condition implies the assumption (H2).”