A CHARACTERIZATION FOR BESOV SPACE AND BLOCH SPACE OF INVARIANT HARMONIC FUNCTION IN THE UNIT BALL

Jinkee Lee (Korea)

Received September 19, 2007

References:

[1] B. R. Choe and Y. J. Lee, On M-harmonic Bloch functions and their Carleson measures, Glasg. Math. J. 40 (1998), 273-289. [2] K. T. Hahn, Bloch-Besov spaces and the boundary behavior of their functions, Notes of the Series of Lecture 21, Seoul National University, 1993. [3] E. G. Kwon, Hyperbolic mean growth of bounded holomorphic functions in the ball, Trans. Amer. Math. Soc. 355 (2002), 1269-1294. [4] E. G. Kwon, A characterization of Bloch space and Besov space, J. Math. Anal. Appl. 324 (2006), 1429-1437. [5] C. Ouyang, W. Yang and R. Zhao, Characterizations of Bergman spaces and Bloch space in the unit ball of Trans. Amer. Math. Soc. 347 (1995), 4301-4313. [6] W. Rudin, Function Theory in the Unit Ball of Springer-Verlag, New York, 1980. [7] M. Stoll, A characterization of Hardy spaces on the unit ball of J. London Math. Soc. 48 (1993), 126-136. [8] M. Stoll, Invariant Potential Theory in the Unit Ball of London Mathematical Society Lecture Notes Series, Vol. 199, Cambridge University Press, 1994. [9] K. Stroethoff, Nevanlinna-type characterizations for the Bloch space and related spaces, Proc. Edinburgh Math. Soc. (2) 33 (1990), 123-141. [10] S. Yamashita, Criteria for functions to be Hardy class Proc. Amer. Math. Soc. 75 (1979), 69-72. [11] K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York and Basel, 1990.

Keywords and phrases: invariant harmonic, Besov space, Bloch space.