TITLE:
Hadamard Gaps and Nk-type Spaces in the Unit Ball
AUTHORS:
M. A. Bakhit, A. E. Shammaky
KEYWORDS:
Nk-type Spaces, Beurling-Type Space, Hadamard Gaps
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.4,
April
25,
2017
ABSTRACT: 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.