Weighted spaces of holomorphic functions on the quarter plane and strip

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, University of Kurdistan, Pasdaran Ave., Postal Code: 66177-15175, Sanandaj, Iran

10.22075/ijnaa.2023.31376.4666

Abstract

In this paper‎, ‎We investigate weighted spaces of holomorphic functions on some subsets of the complex plane such as the quarter plane and a strip in the upper half plane and we obtain isomorphic classification of these weighted spaces‎. ‎Also‎, ‎we characterize the boundedness of composition operators between weighted spaces of holomorphic functions on the quarter plane and strip‎. ‎At last, we study a special subspace of holomorphic functions on the quarter plane.

Keywords

[1] M.A. Ardalani and W. Lusky, Weighted spaces of holomorphic 2π periodic functions on the upper halfplane, Funct. Approx. Comment. Math. 44 (2011), no. 2, 191–201.
[2] M.A. Ardalani and W. Lusky, Bounded operators on weighted spaces of holomorphic functions on the upper halfplane, Studia Math. 209 (2012), no. 3, 225–234.
[3] M.A. Ardalani and W. Lusky, Weighted spaces of holomorphic functions on the upper halfplane, Math. Scand. 111 (2012), no. 2, 244–260.
[4] M.A. Ardalani, Isomorphism classes of weighted spaces of holomorphic functions on some subsets of complex plane, Georgian Math. J. 26 (2019), no. 1, 13–19.
[5] A. Harutyunyan and W. Lusky, A remark on the isomorphic classification of weighted spaces of holomorphic functions on the upper halfplane, Ann. Univ. Sci. Budapest Sect. Comp. 39 (2013), 125–135.
[6] W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc. 51 (1995), 309–320.
[7] W. Lusky, On the isomorphism classes of weighted spaces of harmonic and holomorphic functions, Studia. Math. 75 (2006), no. 1, 19–45.
[8] A.L. Shields and D.L. Willams, Bounded projections, duality and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc. 162 (1971), 287–302.
[9] A.L. Shields and D.L. Willams, Bounded projections and the growth of harmonic conjugates in the unit disc, Mich. Math. J. 29 (1982), 3–25.
[10] M.A. Stanev, Weighted Banach spaces of holomorphic functions in the upper half-plane, arXiv: math.FA/9911082vl, 1999.

Articles in Press, Corrected Proof
Available Online from 19 October 2023
  • Receive Date: 21 August 2023
  • Accept Date: 17 October 2023