Banach-valued multilinear singular integrals

@article{Plinio2015BanachvaluedMS,
  title={Banach-valued multilinear singular integrals},
  author={F. Plinio and Yumeng Ou},
  journal={arXiv: Classical Analysis and ODEs},
  year={2015}
}
We develop a general framework for the analysis of operator-valued multilinear multipliers acting on Banach-valued functions. Our main result is a Coifman-Meyer type theorem for operator-valued multilinear multipliers acting on suitable tuples of UMD spaces. A concrete case of our theorem is a multilinear generalization of Weis' operator-valued H\"ormander-Mihlin linear multiplier theorem. Furthermore, we derive from our main result a wide range of mixed $L^p$-norm estimates for multi-parameter… Expand
Multilinear operator-valued Calder\'on-Zygmund theory
Domination of multilinear singular integrals by positive sparse forms
Multiple Vector Valued Inequalities via the Helicoidal Method
Multi-parameter estimates via operator-valued shifts
Bilinear Calder\'on-Zygmund theory on product spaces
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