University of MaraghehSahand Communications in Mathematical Analysis2322-580702120150601Weighted composition operators between growth spaces on circular and strictly convex domain515612376ENShayestehRezaeiDepartment of Pure Mathematics, Aligudarz Branch, Islamic Azad
University, Aligudarz, Iran.0000-0002-4522-971XJournal Article20141102Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ 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.http://scma.maragheh.ac.ir/article_12376_c69c8af693fb13fb851b69d01a5f63cd.pdf