Jie Xiao (eds.)3540426256, 9783540426257
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. |
Table of contents :
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 |
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