Totally monotone functions with applications to the Bergman space
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Totally monotone functions with applications to the Bergman space

10.2307/2154243

Richards, Kendall C.

20180227

20180227

1993

B, K., R, O. N., K, R., & K, Z. (January 01, 1993). Totally monotone functions with applications to the Bergman space. Transactions of the American Mathematical Society, 337, 2, 795806.

http://collections.southwestern.edu/s/suscholar/item/266

Using a theorem of S. Bernstein [1] we prove a special case of the following maximum principle for the Bergman space conjectured by B. Korenblum [3]: There exists a number S e (0, 1) such that if / and g are analytic functions on the open unit disk D with \f{z)\ < \g{z)\ on 6 < \z\ < 1 then
II/II2 < ll^lh > where  H2 is the L2 norm with respect to area measure on D. We prove the above conjecture when either / or g is a monomial; in this case we show that the optimal constant S is greater than or equal to l/%/3

English

Transactions of the American Mathematical Society

Bergman space

Monotone functions

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