Embedding theorems and integration operators on Bergman spaces with exponential weights

Abstract

In this article, given some positive Borel measure μ, we define two integration operators to be Iμ(f)(z)=∫Df(w)K(z,w)e−2φ(w)dμ(w) and Jμ(f)(z)=∫D|f(w)K(z,w)|e−2φ(w)dμ(w). We characterize the boundedness and compactness of these operators from the Bergman space Aφp to Lφq for 1<p,q<∞, where φ belongs to a large class W0, which covers those defined by Borichev, Dhuez, and Kellay in 2007. We also completely describe those μ’s such that the embedding operator is bounded or compact from Aφp to Lφq(dμ), 0<p,q<∞.