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arXiv · 1503.00850

Some polynomial versions of cotype and applications

Daniel Carando·Andreas Defant·Pablo Sevilla-Peris
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Abstract

We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st and cotype, and that spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get results on convergence of vector-valued power series in infinite many variables and on $\ell_{1}$-multipliers of vector-valued Dirichlet series. Finally we introduce cotype with respect to indexing sets, an idea that includes our previous definitions.

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Daniel Carando, Andreas Defant, Pablo Sevilla-Peris. 2015-03-03. Some polynomial versions of cotype and applications. https://doi.org/10.1016/j.jfa.2015.09.017

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