摘要
We give several equivalences of Bloch functions and little Bloch funetions.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<sup>β</sup>f（z）|<sup>p</sup>（1-|z|<sup>2</sup>）<sup>βp-1</sup>dm（z）is a generalized Carleson measure; f ∈ B<sub>0</sub> if and only if |D<sup>β</sup>f（z）|<sup>p</sup>（1-|z|<sup>2</sup>）<sup>βp-1</sup>dm（z）is a generalized vanishing Carleson measure,where D<sup>β</sup>f（β】0）is the fractional derivative of analytic function f of order β,m denotes the normalised Lebesgue measure.
We give several equivalences of Bloch functions and little Bloch funetions.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<sup>β</sup>f（z）|<sup>p</sup>（1-|z|<sup>2</sup>）<sup>βp-1</sup>dm（z）is a generalized Carleson measure; f ∈ B<sub>0</sub> if and only if |D<sup>β</sup>f（z）|<sup>p</sup>（1-|z|<sup>2</sup>）<sup>βp-1</sup>dm（z）is a generalized vanishing Carleson measure,where D<sup>β</sup>f（β>0）is the fractional derivative of analytic function f of order β,m denotes the normalised Lebesgue measure.
基金
Supported partly by the Yonng Teacher Natural Science Foundation of Shandong Province.
