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Hadamard Gaps and <i>N</i><sub>k</sub>-type Spaces in the Unit Ball
Department of Mathematics, Faculty of Science, Jazan University, Jazan, KSA
Department of Mathematics, Faculty of Science, Jazan University, Jazan, KSA
- 1 Department of Mathematics, Faculty of Science, Jazan University, Jazan, KSA
- 2 Department of Mathematics, Faculty of Science, Jazan University, Jazan, KSA
Advances in Pure Mathematics·Volume 07 (2017)·Pages 306–313·Published 20 April 2017·DOI10.4236/apm.2017.74017
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Abstract
In this paper, we introduce a class of holomorphic Banach spaces N K of functions on the unit ball B of C n . We develop the necessary and sufficient condition for N K ( B ) spaces to be non-trivial and we discuss the nesting property of N K ( B ) spaces. Also, we obtain some characterizations of functions with Hadamard gaps in N K ( B ) spaces. As a consequence, we prove a necessary and sufficient condition for that N K ( B ) spaces coincides with the Beurling-type space.
Keywords<i>N</i><sub>k</sub>-type SpacesBeurling-Type SpaceHadamard Gaps
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