• Li, Songxiao (Department of Mathematics JiaYing University)
  • Received : 2010.06.14
  • Published : 2012.01.31


In this paper we obtain some new characterizations of Besov spaces on the unit ball of $\mathbb{C}^n$. These characterizations are also completely new even in the settings of the unit disk.


  1. K. Hahn and E. Youssfi, Mobius invariant Besov p-spaces and Hankel operators in the Bergman space on the ball in ${\mathbb{C}^{n}$, Complex Variables Theory Appl. 17 (1991), no. 1-2, 89-104.
  2. H. T. Kaptanoglu, Bergman projections on Besov spaces on balls, Illinois J. Math. 49 (2005), no. 2, 385-403.
  3. H. T. Kaptanoglu, Carleson measures for Besov spaces on the ball with applications, J. Funct. Anal. 250 (2007), no. 2, 483-520.
  4. E. G. Kwon, A characterization of Bloch space and Besov space, J. Math. Anal. Appl. 324 (2006), no. 2, 1429-1437.
  5. S. Li and S. Stevic, Some characterizations of the Besov space and the $\alpha$-Bloch space, J. Math. Anal. Appl. 346 (2008), no. 1, 262-273.
  6. S. Li and H. Wulan, Some new characterizations of Bloch spaces, Taiwanese J. Math. 14 (2010), no. 6, 2245-2259.
  7. M. Nowak, Bloch and Mobius invariant Besov spaces on the unit ball of ${\mathbb{C}^{n}$, Complex Variables Theory Appl. 44 (2001), no. 1, 1-12.
  8. W. Rudin, Function Theory in the Unit Ball of ${\mathbb{C}^{n}$, Springer-Verlag, New York, 1980.
  9. K. Stroethoff, The Bloch space and Besov spaces of analytic functions, Bull. Austral. Math. Soc. 54 (1996), no. 2, 211-219.
  10. R. M. Timoney, Bloch functions in several complex variables II, J. Reine Angew. Math. 319 (1980), 1-22.
  11. M. Zhang and W. Xu, Composition operators on $\alpha$-Bloch spaces of the unit ball, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 11, 1991-2002.
  12. K. Zhu, Analytic Besov space, J. Math. Anal. Appl. 157 (1991), no. 2, 318-336.
  13. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.

Cited by

  1. Some characterizations of harmonic Bloch and Besov spaces vol.66, pp.2, 2016,
  2. On characterizations of Bloch spaces and Besov spaces of pluriharmonic mappings vol.2015, pp.1, 2015,