The atomic decomposition of harmonic Bergman functions, dualities and Toeplitz operators
Bull. Korean Math. Soc. 2009 Vol. 46, No. 2, 263-279
Printed March 1, 2009
Young Joo Lee
Chonnam National University
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
MSC numbers : Primary 47B35, Secondary 31B05
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