Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces

Norm and essential norm of an integral‐type operator from the logarithmic Bloch space to the Bloch‐type space on the unit ball

“…Let ||𝜑|| ∞ < 1. Then, as it has been done for the operators in (33), it is proved that P g 𝜑 ∶ X →  𝜇,0 is compact. Hence, ||P…”

“…Product-type operators have attracted considerable attention recently. For some other product-type operators, see, for example, other studies [3][4][5][6][7]14,16,17,[29][30][31][32][33][34][35][36][37][38][39][40] and the related references therein. Let X and Y be Banach spaces and L ∶ X → Y be a bounded linear operator with the norm ||L|| X→Y .…”

Sum of some product‐type operators from Hardy spaces to weighted‐type spaces on the unit ball

“…for each 𝑓 ∈ H p . Let g w (z) = 𝑓 𝜑(w),1 (z), where 𝑓 w,t is defined in (13). By Lemma 4, we have L ∶= sup w∈B ||g w || H p < +∞.…”

“…61) obviously holds. Let ||𝜑|| ∞ = 1 and (z 𝑗 ) 𝑗∈N be a sequence in B such that |𝜑(z 𝑗 )| → 1 as 𝑗 → +∞, and h 𝑗 (z) = 𝑓 𝜑(z 𝑗 ),t (z), where 𝑓 w,t is defined in (13). Then, sup 𝑗∈N ||h 𝑗 || H p < +∞.…”

The differentiation operator on discrete function spaces of a tree

“…With more knowledge of the derivative, operators comprising products of differentiation, multiplication, and composition operators can be further studied. These types of operators are currently being studied when acting on or between many of the classical spaces (see for example [7,10,11,17,18]). In addition, we also hope that new spaces can be identified utilizing the derivative much in the way that the weighted Lipschitz space and the Zygmund space have been.…”