In this paper, we introduce a class of holomorphic Banach spaces NK of functions on the unit ball B of Cn. We develop the necessary and sufficient condition for NK(B) spaces to be non-trivial and we discuss the nesting property of NK(B)?spaces. Also, we obtain some characterizations of functions with Hadamard gaps in NK(B) spaces. As a consequence, we prove a necessary and sufficient condition for that NK(B) spaces coincides with the Beurling-type space.
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