Regularity of Solutions to Extremal Problems in Bergman Spaces

Analysis Seminar
Wednesday, February 16, 2011 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
University of Michigan
I will discuss linear extremal problems in the Bergman spaces $A^p$ ofthe unit disc and a theorem of Ryabykh about regularity of thesolutions to these problems.  I will also discuss extensions I havefound of Ryabykh's theorem in the case where $p$ is an even integer.The proofs of these extensions involve Littlewood-Paley theory and abasic characterization of extremal functions.