Carleson measure characterization of Bloch functions |
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Authors: | Lou Zengjian |
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Institution: | (1) Department of Mathematics, Qufu Normal University, 273165 Qufu, China;(2) Institute of Mathematics, Academia Sinica, 100080 Beijing, China |
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Abstract: | We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D
f(z)|
p
(1-|z|2) p-1
dm(z) is a generalized Carleson measure;f B
0 if and only if |D
f(z)|
p
(1-|z|2) p-1
dm(z) is a generalized vanishing Carleson measure, whereD
f( > 0) is the fractional derivative of analytic functionf of order , m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province. |
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Keywords: | Bloch space Carleson measure Generalized Carleson measure |
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