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TOEPLITZ OPERATORS ON HARDY AND BERGMAN SPACES OVER BOUNDED DOMAINS IN THE PLANE
( Young-bok Chung ),( Heui-geong Na ) 호남수학회 2017 호남수학학술지 Vol.39 No.2
In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.
TOEPLITZ OPERATORS ON HARDY AND BERGMAN SPACES OVER BOUNDED DOMAINS IN THE PLANE
Chung, Young-Bok,Na, Heui-Geong The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.2
In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.
ORTHONORMAL BASIS FOR THE BERGMAN SPACE
Chung, Young-Bok,Na, Heui-Geong The Honam Mathematical Society 2014 호남수학학술지 Vol.36 No.4
We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the or-thonormal basis for the Hardy space consisting of the Szegő kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.
ERRATUM TO: "ORTHONORMAL BASIS FOR THE BERGMAN SPACE" [HONAM MATH. J. 36 (2014), NO. 4, PP. 777-786]
CHUNG, YOUNG-BOK,NA, HEUI-GEONG The Honam Mathematical Society 2015 호남수학학술지 Vol.37 No.3
We modify the normalizing constants of the functions in the orthonormal basis for the Bergman space and restate their consequences in the paper that was published in Honam Math. J. 36 (2014), no. 4, pp. 777-786.