[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2009.46.2.263

THE ATOMIC DECOMPOSITION OF HARMONIC BERGMAN FUNCTIONS, DUALITIES AND TOEPLITZ OPERATORS

Lee, Young-Joo (DEPARTMENT OF MATHEMATICS CHONNAM NATIONAL UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.46, no.2, 2009 , pp. 263-279 More about this Journal

Abstract

On the setting of the unit ball of ${\mathbb{R}}^n$ , we consider a Banach space of harmonic functions motivated by the atomic decomposition in the sense of Coifman and Rochberg [5]. First we identify its dual (resp. predual) space with certain harmonic function space of (resp. vanishing) logarithmic growth. Then we describe these spaces in terms of boundedness and compactness of certain Toeplitz operators.

Keywords

atomic decomposition; harmonic Bergman space; Toeplitz operator;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	B. R. Choe, Note on the Berezin transform on Herz spaces, RIMS Kyokuroku, 21-37, 2006
2	B. R. Choe and Y. J. Lee, A Luecking type subspace, dualities and Toeplitz operators, Acta Math. Hungar. 67 (1995), no. 1-2, 151–170 DOI
3	S. Axler, P. Bourdon, and W. Ramey, Harmonic Function Theory, Springer-Verlag, New York, 1992
4	B. R. Choe, Y. J. Lee, and K. Na, Toeplitz operators on harmonic Bergman spaces, Nagoya Math. J. 174 (2004), 165–186
5	R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^p$ , Representation theorems for Hardy spaces, pp. 11–66, Asterisque, 77, Soc. Math. France, Paris, 1980
6	P. Duren and A. Schuster, Bergman Space, American Mathematical Society, 2004
7	P. Ghatage and S. Sun, A Luecking-type subspace of $L^1_a$ and its dual, Proc. Amer. Math. Soc. 110 (1990), no. 3, 767–774
8	J. Miao, Reproducing kernels for harmonic Bergman spaces of the unit ball, Monatsh. Math. 125 (1998), no. 1, 25–35 DOI
9	M. Pavlovic, Decompositions of $L^p$ and Hardy spaces of polyharmonic functions, J. Math. Anal. Appl. 216 (1997), no. 2, 499–509
10	J. Miao, Toeplitz operators on harmonic Bergman spaces, Integral Equations Operator Theory 27 (1997), no. 4, 426–438 DOI
11	W. K. Hayman and P. B. Kennedy, Subharmonic Functions. Vol. I, London Mathematical Society Monographs, No. 9. Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976
12	M. Jevtic and M. Pavlovic, Harmonic Bergman functions on the unit ball in $R^n$ , Acta Math. Hungar. 85 (1999), no. 1-2, 81–96 DOI
13	S. Perez-Esteva, Duality on vector-valued weighted harmonic Bergman spaces, Studia Math. 118 (1996), no. 1, 37–47
14	P. Ghatage and S. Sun, Duality and multiplication operators, Integral Equations Operator Theory 14 (1991), no. 2, 213–228 DOI