Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
multiplication operator; commutant of an operator; weighted Bergman space
multiplication operator; commutant of an operator; weighted Bergman space
Summary:
We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the \hbox {$n$-dimensional} complex plane. Characterization of the commutant of such operators is given.
References:
[1] Abkar, A.: Norm approximation by polynomials in some weighted Bergman spaces. J. Funct. Anal. 191 (2002), 224-240. DOI 10.1006/jfan.2001.3851 | MR 1911185 | Zbl 1059.30049
[2] Abkar, A.: Application of a Riesz-type formula to weighted Bergman spaces. Proc. Am. Math. Soc. 131 (2003), 155-164. DOI 10.1090/S0002-9939-02-06491-2 | MR 1929035 | Zbl 1037.31002
[3] Abkar, A.: On the commutant of certain operators in the Bergman space. Bull. Malays. Math. Sci. Soc. (2) 35 (2012), 499-502. MR 2912884 | Zbl 1238.47023
[4] Chattopadhyay, A., Das, A. B. Krishna, Sarkar, J., Sarkar, S.: Wandering subspaces of the Bergman space and the Dirichlet space over $\mathbb{D}^n$. Integral Equations Oper. Theory 79 (2014), 567-577. DOI 10.1007/s00020-014-2128-y | MR 3231245 | Zbl 1328.47010
[5] Chung, Y.-B., Na, H.-G.: Toeplitz operators on Hardy and Bergman spaces over bounded domains in the plane. Honam Math. J. 39 (2017), 143-159. DOI 10.5831/HMJ.2017.39.2.143 | MR 3700286 | Zbl 06798549
[6] Dan, H., Huang, H.: Multiplication operators defined by a class of polynomials on $L^2_a(\mathbb{D}^2)$. Integral Equations Oper. Theory 80 (2014), 581-601. DOI 10.1007/s00020-014-2176-3 | MR 3279517 | Zbl 1302.47061
[7] Ding, X., Sang, Y.: The pluriharmonic Hardy space and Toeplitz operators. Result. Math. 72 (2017), 1473-1497. DOI 10.1007/s00025-017-0728-y | MR 3721626 | Zbl 06814121
[8] Douglas, R. G.: Banach Algebra Techniques in Operator Theory. Pure and Applied Mathematics 49, Academic Press, New York (1972). MR 0361893 | Zbl 0247.47001
[9] Duren, P., Schuster, A.: Bergman Spaces. Mathematical Surveys and Monographs 100, American Mathematical Society, Providence (2004). DOI 10.1090/surv/100 | MR 2033762 | Zbl 1059.30001
[10] Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Graduate Texts in Mathematics 199, Springer, New York (2000). DOI 10.1007/978-1-4612-0497-8 | MR 1758653 | Zbl 0955.32003
[11] Shi, Y., Lu, Y.: Reducing subspaces for Toeplitz operators on the polydisk. Bull. Korean Math. Soc. 50 (2013), 687-696. DOI 10.4134/BKMS.2013.50.2.687 | MR 3137713 | Zbl 1280.47039
[12] Zhu, K.: Reducing subspaces for a class of multiplication operators. J. Lond. Math. Soc., II. Ser. 62 (2000), 553-568. DOI 10.1112/S0024610700001198 | MR 1783644 | Zbl 1158.47309
[13] Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics 226, Springer, New York (2005). DOI 10.1007/0-387-27539-8 | MR 2115155 | Zbl 1067.32005
Search
Partner of
