A study on Korenblum conjecture for polynomials of two terms

柯倫布猜想在低項數多項式的一些研究

曾育心(Yu-Shin Tseng)

指導教授 ： 程守慶

國立清華大學/理學院/數學系/碩士(2010年)

https://doi.org/10.6843/NTHU.2010.00087

摘要

Abstract
In 1993, Korenblum, B., O'neil, R., Richards, K., and Zhu, K. [5]
proved a special case of the maximum principle for the Bergman space
conjectured by B. Korenblum [4]: There exists a constant c 2 (0; 1) such
that if f and g are holomorphic functions on the open unit disk D with
jf(z)j jg(z)j on c < jzj < 1 then kfk2 kgk2; where k k2 is the L2 norm
with respect to area measure on D. They proved the above conjecture when
f or g is a monomial. Therefore, we study the conjecture when f and g are
polynomials of one term or two terms, and we will nd the best value for
these special cases.
1

關鍵字

柯倫布

並列摘要

無資料

並列關鍵字

Korenblum

參考文獻

[1] Hayman, W.K., On a conjecture of Korenblum, Analysis, 19(1999), 195-

[2] Hinkkanen, A., On a maximum principle in Bergman space, Journal

[3] Korenblum, B., Transformation of zero sets by contractive operators

[4] Korenblum, B., A maximum principle for the Bergman space, Publ.

functions with applications to the Bergman space, Trans. Amer. Math.