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Full Description
This monograph provides a comprehensive study of a typical and novel function space, known as the $\mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $\mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $\mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $\mathbb{D}$ and open unit ball $\mathbb{B}$ by presenting families of entire functions in the complex plane $\mathbb{C}$ and in higher dimensions. The Theory of $\mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.
Contents
Chapter. 1. Function spaces.- Chapter. 2. The counting function and its applications.- Chapter. 3. Np-spaces in the unit disc D.- Chapter. 4. The alpha-Bloch spaces.- Chapter. 5. Weighted composition operators on D.- Chapter. 6. Hadamard gap series in H.- Chapter. 7. Np spaces in the unit ball B.- Chapter. 8. Weighted composition operators on B.- Chapter. 9. Structure of Np-spaces in the unit ball B.- Chapter. 10. Composition operators between Np and Nq.- Chapter. 11. Np-type functions with Hadamard gaps in the unit ball B.- Chapter. 12. N (p; q; s)-type spaces in the unit ball of Cn.
