Abstract
In this paper we introduce a new class of functions, called \( \mathcal{N}_K \)-type space of analytic functions by the help of a non decreasing function K: [0, ∞)→[0, ∞). Further, under mild conditions on the weight function K we characterize lacunary series in \( \mathcal{N}_K \) space. Finally, we study the boundedness and compactness of composition operators between \( \mathcal{N}_K \) and Bergman spaces.
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Ahmed, A.ES., Bahkit, M.A. (2009). Holomorphic \( \mathcal{N}_K \) and Bergman-type Spaces. In: Grobler, J.J., Labuschagne, L.E., Möller, M. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 195. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0174-0_5
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DOI: https://doi.org/10.1007/978-3-0346-0174-0_5
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