Toeplitz operators on Bloch-type spaces in the unit ball of Cn

Abstract

For 1 α < 2, we consider the Toeplitz operator T μ,α on Bloch-type space B α (B n ) in the unit ball of C n , where μ is a positive Borel measure on B n . We give the necessary and sufficient conditions for T μ,α to be bounded or compact on B α (B n ). Therefore, positive Borel measure μ on B n is completely characterized for which T μ,α is bounded or compact on the Bloch-type space B α (B n ).

On a Sum of More Complex Product-Type Operators from Bloch-Type Spaces to the Weighted-Type Spaces

“…One can see [36] for some results on the Bloch-type spaces. The operators involved Bloch-type spaces, including Toeplitz operators, composition operators, weighted composition operators, products of composition, multiplication and mth differentiation operators, and so on (see, for example, [37][38][39][40][41]).…”

“…By taking the supremum in inequality ( 41) over the unit ball in the space B φ (B), using conditions ( 38) and ( 39), we have that the operator S k,l u, v,ϕ : (41) and the definition of operator norm, we have…”