Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CHARACTERIZATIONS OF BESOV SPACES IN THE UNIT BALL

  • Li, Songxiao (Department of Mathematics JiaYing University)
  • Received : 2010.06.14
  • Published : 2012.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  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. https://doi.org/10.1080/17476939108814499
  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. https://doi.org/10.1016/j.jfa.2006.12.016
  4. E. G. Kwon, A characterization of Bloch space and Besov space, J. Math. Anal. Appl. 324 (2006), no. 2, 1429-1437. https://doi.org/10.1016/j.jmaa.2006.01.052
  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. https://doi.org/10.1016/j.jmaa.2008.05.044
  6. S. Li and H. Wulan, Some new characterizations of Bloch spaces, Taiwanese J. Math. 14 (2010), no. 6, 2245-2259. https://doi.org/10.11650/twjm/1500406073
  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. https://doi.org/10.1080/17476930108815358
  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. https://doi.org/10.1017/S0004972700017676
  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. https://doi.org/10.1007/s10114-007-0993-x
  12. K. Zhu, Analytic Besov space, J. Math. Anal. Appl. 157 (1991), no. 2, 318-336. https://doi.org/10.1016/0022-247X(91)90091-D
  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, https://doi.org/10.1007/s10587-016-0265-y
  2. On characterizations of Bloch spaces and Besov spaces of pluriharmonic mappings vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0884-0