Suppose is an ordered locally convex space, and Hausdorff completely regular spaces and a uniformly bounded, convex and closed subset of . For , let . Then, under some topological and order conditions on , necessary and sufficient conditions are established for the existence of an element in , having marginals and .
For a balanced open subset of a Fréchet space and a dual-Banach space we introduce the topology on the space of holomorphic functions from into . This topology allows us to construct a predual for which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions....
For , let be completely regular Hausdorff spaces, quasi-complete locally convex spaces, , the completion of the their injective tensor product, the spaces of all bounded, scalar-valued continuous functions on , and -valued Baire measures on . Under certain...
We use the Calderón Maximal Function to prove the Kato-Ponce Product Rule Estimate and the Christ-Weinstein Chain Rule Estimate for the Hajłasz gradient on doubling measure metric spaces.
An Orlicz-Pettis type property for vector measures and also the “Uniform Boundedness Principle” are shown to fail without local convexity assumption. The author asks under which generalized convexity hypotheses these properties remain true. This problem is expressed in terms of barrelledness type conditions.