A BMOpλ(D) SPACE, COMPACT TOEPLITZ OPERATORS WITH BMOλ1(D) SYMBOLS ON WEIGHTED BERGMAN SPACES, AND THE BEREZIN TRANSFORM

摘要

Let A2λ(D) stand for the weighted Bergman space on the unit disk D = {z ∈ C : |z| < 1} in C. It consists of analytical in D functions which belong to the weighted space L2λ(D), λ > -1. Here L2λ(D) stands for the space of measurable on D functions f with a finite norm ||f||L2λ(D) = [∫D|f(z)|2dμλ(z)]1/2, dμλ(z)=(λ+1)(1-|z|2)λ1/πdx dy, λ>-1, z=x+iy. The space A2λ(D) is a closed subspace of L2λ(D).