We invent the new notion of coordinatewise multiple summing operators in Banach spaces, and use it to study various vector valued extensions of the well-know Bohnenblust-Hille inequality (which originally extended Littlewood's 4/3-inequality). Our results have application on the summability of monomial coefficients of m-homogeneous polynomials P : ∞ → p , as well as for the convergence theory of products of vector valued Dirichlet series.
Abstract. We estimate the 1-norm N n=1 an of finite Dirichlet polynomials N n=1 ann −s , s ∈ C with coefficients an in a Banach space. Our estimates quantify several recent results on Bohr's strips of uniform but non absolute convergence of Dirichlet series in Banach spaces.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.