borel measure
8.The Carleson-type measures and Toeplitz operators with nonnegative measure symbols on the weighted Bergman space Ap(φ)are investigated. We obtain some equivelent conditions of when a nonnegative Borel measure is Carleson or vanishing Carleson and charicterize the boundedness or compactness of the Toeplitz operators by Carleson or vanishing Carleson measure respectively.
10.We prove that if μ is a nonnegative Borel measure on Ω, then the natural inclusion J:C(Ω)→L 1(μ) is an absolutely summing operator and a Pietsch integral operator with ‖J‖ as =‖J‖ pint =μ(Ω), and the regularity of μ guarantee that the vector measure G:Σ→L 1(μ), defined by G(E)=χ E, is the representation measure of J.

