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

Lee, Young-Joo

• Published : 2009.03.31
• 42 10

#### 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

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