Holomorphic Q Classes
Edition: 1 edition
Publisher: Springer
Published: November 28, 2001
Language: eng
Format: Paperback
Number of pages: 112
ISBN-13: 9783540426257
Subjects: Complex analysis; Functional Analysis; Mathematics; Theory Of Functions; Science/Mathematics; Calculus; Economics - General; General; Business & Economics-Economics - General; Mathematics / Calculus; Mathematics / Functional Analysis; Medical-General; Holomorphic functions
Description: The space Q p consists of all holomorphic functions f on the unit disk for which the L^2 area integrals of its derivative against the p-th power of the Green function of the unit disk are uniformly bounded in the variable that survives the integration. It turns out that Q 1 coincides with BMOA, while, for p>1, Q p are just the Bloch space. For p/in (0,1) the Q p furnish an increasing sequence of spaces, each invariant under conformal mappings of the unit disk onto itself, which interpolate between the Dirichlet space and BMOA. This monograph covers a number of important aspects in complex, functional and harmonic analysis. The primary focus is Q p, p/in (0,1), and their equivalent characterizations. Based on the up-to-date results obtained by experts in their respective fields, each of the eight chapters unfolds from the basics to the more complex. The exposition here is rapid-paced and efficient, with proofs and examples.
Notes: Lecture Notes in Mathematics