Harmonic Analysis

L^p boundedness of the Bergman projection on a worm domain

speaker: Marco Maria Peloso (Università di Milano)

abstract: (This is joint work with Steven Krantz.) In this seminar I will consider a non-smooth, unbounded version of the Deiderich-Fornaess worm domain, D_\beta. It is known that on such domains the Bergman projection does not preserve the Sobolev space W^k, when k is larger than a certain k₀ depeding on the winding of the domain. I will indicate how to compute the asymptotic expansion of the Bergman kernelon D_\beta. Having such an expansion, it is possible to determine the exact range of p's for which the Bergman projection is a bounded operator on the Lebesgue space L^p(D_\beta).

<< Go back