Weighted Bergman projections and kernels: $L^p$ regularity and zeros
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- by Yunus E. Zeytuncu
- Proc. Amer. Math. Soc. 139 (2011), 2105-2112
- DOI: https://doi.org/10.1090/S0002-9939-2010-10795-5
- Published electronically: December 1, 2010
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Abstract:
We investigate $L^p$ regularity of weighted Bergman projections and zeros of weighted Bergman kernels for the weights that are radially symmetric and comparable to 1 on the unit disc.References
- Harold P. Boas, The Lu Qi-Keng conjecture fails generically, Proc. Amer. Math. Soc. 124 (1996), no. 7, 2021–2027. MR 1317032, DOI 10.1090/S0002-9939-96-03259-5
- Harold P. Boas, Lu Qi-Keng’s problem, J. Korean Math. Soc. 37 (2000), no. 2, 253–267. Several complex variables (Seoul, 1998). MR 1775958
- Harold P. Boas, Siqi Fu, and Emil J. Straube, The Bergman kernel function: explicit formulas and zeroes, Proc. Amer. Math. Soc. 127 (1999), no. 3, 805–811. MR 1469401, DOI 10.1090/S0002-9939-99-04570-0
- Stephen M. Buckley, Pekka Koskela, and Dragan Vukotić, Fractional integration, differentiation, and weighted Bergman spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999), no. 2, 369–385. MR 1670257, DOI 10.1017/S030500419800334X
- Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Étude de certaines intégrales singulières. MR 0499948
- Peter Duren and Alexander Schuster, Bergman spaces, Mathematical Surveys and Monographs, vol. 100, American Mathematical Society, Providence, RI, 2004. MR 2033762, DOI 10.1090/surv/100
- Frank Forelli and Walter Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974/75), 593–602. MR 357866, DOI 10.1512/iumj.1974.24.24044
- Ewa Ligocka, On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), no. 3, 257–272. MR 1019793, DOI 10.4064/sm-94-3-257-272
- I. Ramadanov, Sur une propriété de la fonction de Bergman, C. R. Acad. Bulgare Sci. 20 (1967), 759–762 (French). MR 226042
- Yunus E. Zeytuncu. ${L}^p$ and Sobolev Regularity of Weighted Bergman Projections. Ph.D. Thesis, The Ohio State University, 2010.
- Kehe Zhu, Operator theory in function spaces, 2nd ed., Mathematical Surveys and Monographs, vol. 138, American Mathematical Society, Providence, RI, 2007. MR 2311536, DOI 10.1090/surv/138
Bibliographic Information
- Yunus E. Zeytuncu
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 796075
- Email: yunus@math.ohio-state.edu; zeytuncu@math.tamu.edu
- Received by editor(s): June 4, 2010
- Published electronically: December 1, 2010
- Communicated by: Richard Rochberg
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2105-2112
- MSC (2010): Primary 30H20, 32A36; Secondary 47B32
- DOI: https://doi.org/10.1090/S0002-9939-2010-10795-5
- MathSciNet review: 2775388