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

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