Carleson type measures on parabolic Bergman spaces

Abstract

Let b^p_α, 0<α≤1, be the parabolic Bergman space, the Banach space of solutions of parabolic equations (∂/∂ t+(-Δ)^α)u=0 on the upper half space Rⁿ⁺¹₊ which have finite L^p norms. We study Carleson type measures on b^p_α and give a necessary and sufficient condition for a measure μ on Rⁿ⁺¹₊ to be of Carleson type on b^p_α. As an application, we characterize bounded Toeplitz operators in the space b²_α.