Multipliers of Fractional Cauchy Transforms and Smoothness Conditions
1998 ◽
Vol 50
(3)
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pp. 595-604
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AbstractThis paper studies conditions on an analytic function that imply it belongs to Mα, the set of multipliers of the family of functions given by where μ is a complex Borel measure on the unit circle and α > 0. There are two main theorems. The first asserts that if 0 < α < 1 and sup. The second asserts that if 0 < α < 1, ƒ ∈ H∞ and supt. The conditions in these theorems are shown to relate to a number of smoothness conditions on the unit circle for a function analytic in the open unit disk and continuous in its closure.
2000 ◽
Vol 24
(9)
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pp. 577-581
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1969 ◽
Vol 35
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pp. 151-157
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