$L^p$ regularity of weighted Bergman projections
HTML articles powered by AMS MathViewer
- by Yunus E. Zeytuncu PDF
- Trans. Amer. Math. Soc. 365 (2013), 2959-2976 Request permission
Abstract:
We investigate $L^p$ regularity of weighted Bergman projections on the unit disc and $L^p$ regularity of ordinary Bergman projections in higher dimensions.References
- David E. Barrett, Irregularity of the Bergman projection on a smooth bounded domain in $\textbf {C}^{2}$, Ann. of Math. (2) 119 (1984), no. 2, 431–436. MR 740899, DOI 10.2307/2007045
- David Bekollé and Aline Bonami, Inégalités à poids pour le noyau de Bergman, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 18, A775–A778 (French, with English summary). MR 497663
- 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
- Alexander Borichev, On the Bekollé-Bonami condition, Math. Ann. 328 (2004), no. 3, 389–398. MR 2036327, DOI 10.1007/s00208-003-0488-8
- David Barrett and Sönmez Şahutoğlu. Irregularity of the Bergman projection on worm domains in $\mathbb {C}^n$. Preprint, 2010.
- Philippe Charpentier and Yves Dupain, Estimates for the Bergman and Szegö projections for pseudoconvex domains of finite type with locally diagonalizable Levi form, Publ. Mat. 50 (2006), no. 2, 413–446. MR 2273668, DOI 10.5565/PUBLMAT_{5}0206_{0}8
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250
- Milutin R. Dostanić, Unboundedness of the Bergman projections on $L^p$ spaces with exponential weights, Proc. Edinb. Math. Soc. (2) 47 (2004), no. 1, 111–117. MR 2064739, DOI 10.1017/S0013091501000190
- 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
- Håkan Hedenmalm, The dual of a Bergman space on simply connected domains, J. Anal. Math. 88 (2002), 311–335. Dedicated to the memory of Tom Wolff. MR 1979775, DOI 10.1007/BF02786580
- Steve G. Krantz and Marco M. Peloso, New results on the Bergman kernel of the worm domain in complex space, Electron. Res. Announc. Math. Sci. 14 (2007), 35–41. MR 2336324
- Steven G. Krantz and Marco M. Peloso, The Bergman kernel and projection on non-smooth worm domains, Houston J. Math. 34 (2008), no. 3, 873–950. MR 2448387
- 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
- Loredana Lanzani and Elias M. Stein, Szegö and Bergman projections on non-smooth planar domains, J. Geom. Anal. 14 (2004), no. 1, 63–86. MR 2030575, DOI 10.1007/BF02921866
- Jeffery D. McNeal, The Bergman projection as a singular integral operator, J. Geom. Anal. 4 (1994), no. 1, 91–103. MR 1274139, DOI 10.1007/BF02921594
- J. D. McNeal and E. M. Stein, Mapping properties of the Bergman projection on convex domains of finite type, Duke Math. J. 73 (1994), no. 1, 177–199. MR 1257282, DOI 10.1215/S0012-7094-94-07307-9
- Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
- D. H. Phong and E. M. Stein, Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains, Duke Math. J. 44 (1977), no. 3, 695–704. MR 450623, DOI 10.1215/S0012-7094-77-04429-5
- Zbigniew Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), no. 1, 110–134. MR 1077547, DOI 10.1016/0022-1236(90)90030-O
- Yunus E. Zeytuncu. $L^p$ regularity of some weighted Bergman projections on the unit disc. Preprint, 2010.
- Yunus E. Zeytuncu, Weighted Bergman projections and kernels: $L^p$ regularity and zeros, Proc. Amer. Math. Soc. 139 (2011), no. 6, 2105–2112. MR 2775388, DOI 10.1090/S0002-9939-2010-10795-5
- 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
Additional Information
- Yunus E. Zeytuncu
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 796075
- Email: zeytuncu@math.tamu.edu
- Received by editor(s): July 6, 2010
- Received by editor(s) in revised form: June 8, 2011
- Published electronically: November 7, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 2959-2976
- MSC (2010): Primary 32A25, 32A36; Secondary 32A30
- DOI: https://doi.org/10.1090/S0002-9947-2012-05686-8
- MathSciNet review: 3034455