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      Strong pseudoconvexity in Banach spaces

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          Abstract

          Having been unclear how to define strong (or strict) pseudoconvexity in the infinite-dimensional and non-smooth boundary context, we take a look at the available literature on strong pseudoconvexity, focusing first in eliminating the need of two degress of smoothness e.g. via distributions. We pass to the infinite-dimensional setting by first seeing a uniform notion of strict pseudoconvexity. Since \(2\)-uniformly PL-convex Banach spaces play an important role as examples with uniformly pseudoconvex unit ball, we briefly show that \(r\)-uniformly convex spaces are \(r\)-uniformly PL-convex, and prove a number of characterizations of \(r\)-uniform PL-convexity.

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          Sharp uniform convexity and smoothness inequalities for trace norms

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            Logarithmic Sobolev inequalities and hypercontractive estimates on the circle

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              Domaines pseudoconvexes infinis et la m\'etrique riemannienne dans un espace projectif

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                Author and article information

                Journal
                2017-01-13
                Article
                1701.03823

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                32T15, 32C15, 46B25, 32A70
                17 pages
                math.CV

                Analysis

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