Seminar on Banach and Metric Space Geometry

Date: September 13, 2018

Time: 5:00PM - 5:50PM

Location: BLOC 220

Speaker: Michal Wojciechowski, IMPAN, Warsaw

Title: On yet another analogon of Riesz brothers theorem for Sobolev space

Abstract: We show that the quotient space BV/W^1,1 is isomorphic to the space of bounded borel measures. Here BV denotes the space of functions of bounded variation and W^1,1 the Sobolev space of functions with integrable gradient on regular domain. One can see this as an analogon of Pełczyński's result that dual to the space of C¹-smooth functions is a separable perturbation of the space of measures. Main ingredients of a proof are G. Alberti rank one theorem and extension/averaging results for Sobolev and BV spaces