Overview

This monograph provides a comprehensive study of a typical and novel function space, known as the ℓ_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.

Spaces Covered

The authors introduce various weighted spaces, including the classical Hardy space H², Bergman space B², and Dirichlet space ℓ. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces 𝓪^p and Bergman-type spaces A^p.

Extensions and Applications

Additionally, the authors extend their analysis beyond the open unit disk ℝ and open unit ball 𝓡 by presenting families of entire functions in the complex plane ℂ and in higher dimensions. The Theory of ℓ_p Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.