Weighted composition operators between growth spaces on circular and strictly convex domain - Shayesteh Rezaei (Sahand Communications in Mathematical Analysis, 2015)
Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcalH(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcalA^omega(Omega_X)$ is the space of all $finmathcalH(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the Minkowski functional on $Omega_X$ and $omega :[0,1)rightarrow(0,infty)$ is a nondecreasing, continuous and unbounded function. Boundedness and compactness of weighted composition operators between growth spaces on circular and strictly convex domains were investigated.