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.
Author(s): Jie Xiao (eds.)
Series: Lecture Notes in Mathematics 1767
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2001
Language: English
Pages: 104
City: Berlin; New York
Tags: Functions of a Complex Variable; Potential Theory
Fundamental Material....Pages 1-12
Composite Embedding....Pages 13-22
Series Expansions....Pages 23-34
Modified Carleson Measures....Pages 35-44
Inner-Outer Structure....Pages 45-56
Pseudo-holomorphic Extension....Pages 57-66
Representation via ∂-equation....Pages 67-86
Dyadic Localization....Pages 87-104