AASCIT - Journal - All Issues

ISSN: 2375-3927

International Journal of Mathematical Analysis and Applications

The Journal

Manuscript Information

Product of Extended Cesáro Operator and Composition Operator from B^α to Q_k (p,q) Spaces

International Journal of Mathematical Analysis and Applications
Vol.4 , No. 6, Publication Date: Nov. 16, 2017, Page: 47-51

750 Views Since November 16, 2017, 318 Downloads Since Nov. 16, 2017

Paper in PDF (257K)

Follow on

Authors

[1]	A. Kamal, Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt.
[2]	T. I. Yassen, Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt.

Abstract

In this paper, we study the properties boundedness and compactness of product of extended Cesáro operator and composition operator from the Bloch-type spaces B^α to Q_k (p,q) spaces on the unit ball of Cⁿ Moreover, necessary and sucient conditions are given for The product of extended Cesáro operator and composition operator from the Bloch-type spaces B^α to Q_k (p,q) spaces to be bounded and compact.

Keywords

Extended Cesáro Operator, Composition Operator, Boundedness and the Compactness

Reference

[01]	J. Arazy, D. Fisher and J. Peetre, Möbius invariant function spaces, J. Reine Angew. Math. 363 (1986), 110-145.
[02]	R. Aulaskari and P. Lappan, Criteria for an analytic function to be Bloch and a harmonic or meromorphic function to be normal, Complex Analysis and its applications, Pitman Research Notes in Math. 305, Longman Scientific and Technical Harlow, (1994), 136-146.
[03]	A. El-Sayed Ahmed and M. A. Bakhit, Composition operators on some holomorphic Banach function spaces, Math. Scand. 104 (2) (2009), 275-295.
[04]	M. Essén, H. Wulan, and J. Xiao, Several function-theoretic characterizations of Möbius invariant spaces, J. Funct. Anal. 230 (2006), 78-115.
[05]	Z. S. Fang, Z. H. Zhou, Extended Cesàro operators from weighted Bloch spaces to Zygmund spaces in the unit ball, J. Math. Anal. Appl. 359 (2) (2009) 499-507.
[06]	Z. S. Fang, Z. H. Zhou, Extended Cesàro operators on BMOA spaces in the unit ball, J. Math. Inequal. 4 (1) (2010) 27-36.
[07]	D. Gu, Extended Cesàro operators from logarithmic-type spaces to Bloch-type spaces, Abstr. Appl. Anal. 2009, 9p, Article ID 246521.
[08]	Z. J. Hu, Extended Cesàro operators on mixed norm spaces, Proc. Amer. Math. Soc. 131 (7) (2003) 2171-2179.
[09]	A. Kamal, A. El-Sayed Ahmed and T. I. Yassen, Quasi-metric spaces and composition operators on and spaces, J. Comp. Theoretical Nanoscience. 12 (8) (2015), 1795-1801.
[10]	A. Kamal, and T. I. Yassen, Some Properties of Composition Operator Acting Between General Hyperbolic Type Spaces, Int. J. Math. Anal. Appl. 2 (2) (2015), 17-26.
[11]	S. Li and H. Wulan, Composition operators on spaces, J. Math. Anal. Appl. 327 (2007), 948-958.
[12]	Yu-Xia Liang, Ze-Hua Zhou, Product of Extended Cesàro Operator and Composition Operator from Lipschitz Space to Space on the Unit Ball. Abstr, Appl. Anal. 2011, 9 p, Article ID 152635.
[13]	LÜ Xiao-fen, Weighted composition operators from spaces to Bers-type spaces in the unit ball, Appl. Math. J. Chinese Univ., 24 (4) (2009), 462-472.
[14]	J. Shi, Inequalities for the integral means of holomorphic function and their derivatives in the unit ball of , Trans Amer Math Soc. 328 (1991), 619-637.
[15]	S. Stevi , On operator from the logarithmic Bloch-type space to the mixed-norm space on the unit ball, Appl. Math. Comput. 215 (2010) 4248-4255.
[16]	M. Tjani, Compact composition operators on Besov spaces, Trans. Amer. Math. Soc. 355 (2003), 4683-4698.
[17]	H. Wulan and J. Zhou, type spaces of analytic functions. J. Funct. Spaces Appl. 4 (1) (2006), 73-84.
[18]	H. Wulan and Y. Zhang, Hadamard products and spaces, J. Math. Anal. Appl, 337 (2) (2008), 1142-1150.
[19]	R. Zhao, On a general family of function spaces, Ann. Acad. Sci. Fenn. Series A I. Mathematica. Dissertationes. 105. Helsinki: Suomalainen Tiedeakatemia, (1996), 1-56.
[20]	R. Zhao, On -Bloch functions and VMOA, Acta. Math. Sci, 3 (1996), 349 - 360.