Generalized composition operators from logarithmic Bloch type spaces to Q_K type spaces

Subject Areas : Applied Mathematics

Sh. Rezaei ¹ , H. Mahyar ²

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Kharazmi (Tarbiat Moallem) University, Tehran, Iran.

Received: 2011-07-25 Accepted : 2012-04-17 Published : 2014-05-01

Keywords:

Abstract :

In this paper boundedness and compactness of generalized composition oper-ators from logarithmic Bloch type spaces to Q_K type spaces are investigated.

References:

[1] A. Baernstein II, Analytic functions of bounded mean oscillation, Aspects
of contemporary complex analysis, Academic Peress, London, (1980) 3-36.
[2] J. B. Conway, Functions of One Complex Variable, Spinger-Verlag, New
York, 1978.
[3] M. Darus and R. W. Ibrahim, Integral operator dened by K-th Hadamard
product of hypergeometric functions, Mathematics Scientic Journal (MSJ),
Vol. 4, No. 2, S. N. 9, (2009) 59-73.
[4] M. Essen and H.Wulan, On analytic and meromorphic functions and spaces
of QK type, Illinois J. Math. 46 (4) (2002) 1233-1258.
[5] H. Li, P. Liu and M. Wang, Composition operators between generally
weighted Bloch spaces of polydisk, J. Inequal. Pure Appl. Math. 8 (3) (2007),
Article 85, 1-8.
[6] S. Li and S. Stevic, Generalized composition operators on Zygmund spaces
and Bloch type spaces, J. Math. Anal. Appl. 338 (2) (2008) 1282-1295.
[7] H. Mahyar and Sh. Rezaei, Generalized composition and Volterra type
operators between QK spaces, Quaestiones Mathematicae. 35 (1) (2012).
[8] Sh. Rezaei and H. Mahyar, Essential norm of generalized composition
operators from weighted Dirichlet or Bloch type space to QK type space,
Bull. Iranian Math. Soc. to appear.
[9] S. Stevic, On new Bloch type spaces, Appl. Math. Compute, 215 (2009)
841-849.
[10] H. Wulan and J. Zhou, QK type spaces of analytic functions, J. Function
Spaces and Applications, 4 (1) (2006) 73-84.
[11] H. Wulan, K. Zhu, Lacunary series in QK spaces, Studia. Math. 178 (3)
(2007) 217-230.
[12] H. Wulan and P. Wu, Characterization of QT spaces, J. Math. Ana. Appl.
254 (2001) 484-497.
[13] J. Xiao, Holomorphic Q Classes, Lecture Notes in Mathematics, Vol. 1767,
Springer-Verlag, Berlin, Heidelberg, 2001.

[14] F. Zhang and Y. Liu, Generalized composition operators from Bloch type
spaces to QK type spaces, Jurnal of Function Spaces and Applications, 8 (1)
(2010), 55-66.
[15] R. Zhao, On a general family of function spaces, Ann. Acad. Sci. Fenn.
Math. Diss, 105 (1996) 1-56.
[16] K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Graduate texts
in Mathematics, Vol. 226, Springer, New York, 2005.