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The aim of this short note is to prove the equivalence of certain definitions of solutions to an evolution variational inequality in metric spaces, introduced by Ambrosio, Gigli, Savaré, and Daneri, Savaré.
We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.
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