Atomic decomposition for <italic>μ</italic>-Bloch space in C<sup><italic>n</italic></sup>

Abstract

Let μ be a normal function on [0; 1). In this paper, we discuss several problems on the normal weight Bloch type space β μ ( B ) in the unit ball B. First, we give an integral representation for functions in β μ ( B ). Second, we prove that β μ ( B ) can be identi ed with the dual space of the normal weight Bergman type space A ν 1 ( B ). Finally, we give and prove the main result, i.e., every function in the μ -Bloch space β μ ( B ) can be decomposed into a series of very nice functions (called atoms).