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Lp and Sobolev Regularity of Weighted Bergman Projections
Zeytuncu, Yunus Ergin

2010, Doctor of Philosophy, Ohio State University, Mathematics.

The weighted Bergman projection is the orthogonal projection operator from the space of square integrable functions onto the space of square integrable holomorphic functions on a suitable domain and weight pair (Omega, mu). Initially, projection operators are defined on L2 spaces but their behavior on other function spaces, e.g. Lp, Sobolev and Hölder spaces, is of considerable interest.


In the first part of this dissertation, we investigate Lp and Sobolev mapping properties of weighted Bergman projections on the unit disc of the complex plane. In the second part, we use Forelli and Rudin's inflation principle to extend the weighted results in one dimension to unweighted results in higher dimensions.

Jeffery McNeal (Advisor)
Kenneth Koenig (Committee Member)
Yuan Lou (Other)

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Zeytuncu, Y. (2010). Lp and Sobolev Regularity of Weighted Bergman Projections. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Zeytuncu, Yunus. "Lp and Sobolev Regularity of Weighted Bergman Projections." Electronic Thesis or Dissertation. Ohio State University, 2010. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Zeytuncu, Yunus "Lp and Sobolev Regularity of Weighted Bergman Projections." Electronic Thesis or Dissertation. Ohio State University, 2010. https://etd.ohiolink.edu/

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