Functional Analysis and Applications Seminar 

14/05/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building
Stefan Samko, Universidade do Algarve, Faro

Potential operators in generalized Hölder spaces over domains without the cancellation property

We study potential operators in Hölder-type spaces over uniform domains in the Euclidean space and show that they map the subspace of functions vanishing at the boundary into the improved Hölder-type space The problem in the study is related to the absence of the so called cancellation property for domains, our proofs being based on a special treatment of the potential of a constant function and the usage of the uniformity of domains (Jones domains). The talk is based on a joint work with Lars Diening.