An Integral Formula in Weighted Bergman Spaces

作者：Weir Rachel J^*

来源：Computational Methods and Function Theory, 2010, 10(1): 265-279.

• Bergman space
• biharmonic Green function
• extremal function
• contractive divisor
• expansive multiplier
• inner function

In order to establish that extremal functions in the Bergman space A(p) act as both expansive multipliers and contractive divisors, Duren, Khavinson, Shapiro and Sundberg made use of an integral formula involving the biharmonic Green function. Using a weighted biharmonic Green function, we derive an analogous integral formula in the standard weighted Bergman space A(alpha)(p) when alpha = 1, and we also discuss how the formula can be established for general alpha. Moreover, we show that each A(1)(p) inner function acts as a contractive divisor on the invariant subspace which it generates.

• 出版日期2010