Toeplitz operators on the space of analytic functions with logarithmic growth

Continuous and compact Toeplitz operators for positive symbols are characterized on the space H V ∞ of analytic functions with logarithmic growth on the open unit disc of the complex plane. The characterizations are in terms of the behaviour of the Berezin transform of the symbol. The space H V ∞ was introduced and studied by Taskinen. The Bergman projection is continuous on this space in a natural way, which permits to define Toeplitz operators. Sufficient conditions for general symbols are also presented.