Properties of Weighted Composition Operators on Some Weighted Holomorphic Function Classes in the Unit Ball

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A. E. Shammaky, M. A. Bakhit, Properties of Weighted Composition Operators on Some Weighted Holomorphic Function Classes in the Unit Ball, Int. J. Anal. Appl., 12 (2) (2016), 87-97.

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A. E. Shammaky, M. A. Bakhit

Abstract

In this paper, we introduce NK-type spaces of holomorphic functions in the unit ball of C n by the help of a non-decreasing function K: (0,∞) → [0,∞). Several important properties of these spaces in the unit ball are provided. The results are applied to characterize boundedness and compactness of weighted composition operators Wu,φ from NK (B) spaces into Beurling-type classes. We also find the essential norm estimates for Wu,φ from NK(B) spaces into Beurling-type classes.

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References

  1. M.A. Bakhit, A.E. Shammaky, Predual Norms of Some Holomorphic Function Spaces, International J. Functional Analysis, Operator Theory and Applications, 6(3) (2014), 153-176.
  2. C.C. Cowen and B.D. MacCluer, Composition operators on spaces of analytic functions, CRC Press, 1995.
  3. P. Duren and R. Weir, The pseudohyperbolic metric and Bergman spaces in the ball, Trans. Amer. Math. Soc. 359 (2007), 63-76.
  4. A. El-Sayed Ahmed and M.A. Bakhit, Holomorphic N K and Bergman-type spaces, Birkhuser Series on Operator Theory: AdVances and Applications (2009), BirkhuserVerlag Publisher BaselSwitzerland, 195 (2009), 121-138.
  5. A. El-Sayed Ahmed and M.A. Bakhit, Composition operators acting betweensome weighted Möbius invariant spaces, J. Ann. Funct. Anal. 2 (2011), 138-152.
  6. B. Hu and L.H. Khoi, Compact difference of weighted composition operators on N p -spaces in the ball, Romanian J. Pure Appl. Math. 60(2) (2015), 101-116.
  7. S. Krantz, Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.
  8. W. Rudin, Function Theory in the Unit Ball of C n , Springer-Verlag, New York, 1980.
  9. A.E. Shammaky, Weighted composition operators acting between kind of weighted Bergman-type spaces and the Bers-type space, International Journal of Mathematical, Computational Science and Engineering, 8(3) (2014), 496- 499.
  10. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2004.