Analysis seminar
Friday, Feb 9, 4 pm – 5 pm
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Venue: Ramanujan Hall
Host: Chandan Biswas
Speaker: Debraj Chakrabarti
Affiliation: Central Michigan University, Mt. Pleasant, MI
Title: Projection operators on Bergman spaces of Reinhardt domains.
Abstract: It is a famous result of M. Riesz that the Szegö projection operator, initially defined as the orthogonal projection from the space of square integrable functions on the circle to the Hardy space of the disc extends continuously as a projection operator from onto. There is a long history of similar results in the setting of Bergman spaces, and a long list of domains where an analogous statement does not hold in the Bergman setting. We try to understand the geometric distinction between the Hardy and the Bergman situations on Lebesgue spaces, and propose a new projection operator on Reinhardt domains which is expected to have better mapping properties. We verify that the new operator satisfies Lebsegue space estimates in some situations where the Bergman projection operator does not satisfy such estimates. This is joint work with Luke Edholm of the University of Vienna.