DERIVATIVES OF INNER FUNCTIONS IN BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

作者：Perez Gonzalez Fernando^*; Rattya Jouni; Reijonen Atte

来源：Annales Academiae Scientiarum Fennicae-Mathematica, 2017, 42(2): 735-753.

DOI：10.5186/aasfm.2017.4248

• Bergman space
• Blaschke product
• doubling weight
• inner function

We find a condition for the zeros of a Blaschke product B which guarantees that B' belongs to the Bergman space A(omega)(p) induced by a doubling weight w, and show that this condition is also necessary if the zero-sequence of B is a finite union of separated sequences. We also give a general necessary condition for the zeros when B' is an element of A(omega)(p), and offer a characterization of when the derivative of a purely atomic singular inner function belongs to A(omega)(p)).

• 出版日期2017