Carleson Measures and Toeplitz Operators on Doubling Fock Spaces

Abstract

Given ϕ a subharmonic function on the complex plane ℂ, with ΔϕdA being a doubling measure, the author studies Fock Carleson measures and some characterizations on μ such that the induced positive Toeplitz operator Tμ is bounded or compact between the doubling Fock space $$F_\phi ^p$$ and $$F_\phi ^\infty $$ with 0 < p ≤ ∞, where μ is a positive Borel measure on ℂ.