On some product-type operators from Hardy–Orlicz and Bergman–Orlicz spaces to weighted-type spaces

Generalized product-type operators from weighted Bergman–Orlicz spaces to Bloch–Orlicz spaces

“…We assume that ∈ U s such that p ∈ L r . Under this assumption, A p α is a complete metric space (see [27]). For the sake of convenience, we write…”

“…Next we present some facts on weighted Bergman-Orlicz spaces from [27]. The function ≡ 0 is called a growth function, if it is a continuous and nondecreasing function from the interval [0, +∞) onto itself.…”

Product-Type Operators From Weighted Bergman-Orlicz Spaces to Weighted Zygmund Spaces

“…From the proof of Theorem 3.6 in [20], the sequence {g n,2 } n∈N uniformly converges to zero on any compact subset of D as n → ∞. Then by Lemma 2.1,…”

“…We introduce the needed spaces and facts in [20]. The function Φ ≡ 0 is called a growth function, if it is a continuous and nondecreasing function from the interval [0, ∞) onto itself.…”

“…This paper is devoted to characterizing the boundedness and compactness of the operator W ϕ,ψ D from weighted Bergman-Orlicz spaces to weighted Zygmund spaces. It can be regarded as a continuation of the investigation of operators from weighted Bergman-Orlicz spaces to other spaces (see, e.g., [20]). …”