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Title
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Totally monotone functions with applications to the Bergman space
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Description
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10.2307/2154243
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Creator
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Richards, Kendall C.
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Date
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2018-02-27
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Date Available
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2018-02-27
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Date Issued
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1993
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Identifier
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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, 795-806.
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uri
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http://collections.southwestern.edu/s/suscholar/item/266
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Abstract
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Using a theorem of S. Bernstein [1] we prove a special case of the following maximum principle for the Bergman space conjectured by B. Koren-blum [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
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Language
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English
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Publisher
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Transactions of the American Mathematical Society
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Subject
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Bergman space
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Monotone functions
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Type
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Article
