Previous |  Up |  Next

Article

Keywords:
weighted Bergman space; sub-Bergman Hilbert space; weighted Toeplitz operator; reproducing kernel
Summary:
We study sub-Bergman Hilbert spaces in the weighted Bergman space $A^2_\alpha $. We generalize the results already obtained by Kehe Zhu for the standard Bergman space $A^2$.
References:
[1] Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Graduate Texts in Mathematics, Vol. 199, Springer-Verlag, New York (2000). DOI 10.1007/978-1-4612-0497-8_1 | MR 1758653 | Zbl 0955.32003
[2] Sarason, D.: Sub-Hardy Hilbert Spaces in the Unit Disk. John Wiley and Sons Inc., New York (1994). MR 1289670
[3] Saitoh, S.: Thoery of Reproducing Kernels and its Applications. Pitman Research Notes in Mathematics, Vol. 189, New York (1988). MR 0983117
[4] Sultanic, S.: Sub-Bergman Hilbert spaces. J. Math. Anal. Appl. 324 (2006), 639-649. DOI 10.1016/j.jmaa.2005.12.035 | MR 2262497 | Zbl 1115.46021
[5] Zhu, K.: Sub-Bergman Hilbert spaces in the unit disk. Indiana Univ. Math. J. 45 (1996), 165-176. MR 1406688
[6] Zhu, K.: Sub-Bergman Hilbert spaces in the unit disk II. J. Func. Anal. 202 (2003), 327-341. DOI 10.1016/S0022-1236(02)00086-1 | MR 1990528 | Zbl 1039.47019
[7] Zhu, K.: Operator Theory in Function Spaces. Dekker, New York (1990). MR 1074007 | Zbl 0706.47019
Partner of
EuDML logo