Abstract
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