Document Type : Research Paper


Department of Pure Mathematics, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran.


Let $\Omega_X$ 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 $f\in\mathcal{H}(\Omega_X)$ for which $$|f(x)|\leqslant C \omega(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$ 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.


[1] E. Abakumov and E. Doubtsov,Reverse estimates in growth spaces, Mathematische Zeitschrift, 271 (2012) 392-413.
[2] l K. D. Bierstedt, J. Bonet and J. Taskinen, Associated weights and spaces of holomorphic functions, Studia Math. 127 (2) (1998) 137-168.
[3] l J. Bonet, P. Domanski, M. Lindstrom and J. Taskinen, Composition operators between weighted Banach spaces of analytic functions, J. Aust. Math. Soc. (Ser. A),64 (1998) 101-118.
[4] lJ. B. Conway,A Course in Functional Analysis, Spinger-Verlag New York, 1985.
[5] E. Doubstov, Growth spaces on circular domains: Composition operators and Carleson measure, Comptes Rendus Mathematigue, 347 (2009), 609-611.
[6] E. Doubtsov, Carleson-Sobolev measure for weighted Bloch spaces, Func. Anal. 258 (2010) 2801-2816.
[7] E. S. Dubtsov, Weighted composition operators on growth spaces, Siberian Mathematical Journal, 50 ( 6) (2009) 998-1006.
[8] W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc., 51 (1995) 309-320.
[9] A. Montes-Rodrguez,Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc., 61 (2) (2000) 872-884.
[10] J. Mujica, Complex Analysis in Banach Spaces, Elsevier Science Publishing Company, 1985.
[11] G. Patrizio, Parabolic exhaustions for strictly convex domains, Manuscripta Math. 47 (1984) 271-309.
[12] E. Zeidler, Applied Functional Analysis Applications to Mathematical Physics, Applied Mathematical Sciences, Springer-Verlag New Yorc Inc. V. 108.