Bulletin of the
Korean Mathematical Society BKMS

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