Holomorphic Q Classes / Lecture Notes in Mathematics Bd.1767 (PDF)

Name: Holomorphic Q Classes / Lecture Notes in Mathematics Bd.1767
Brand: Springer Berlin Heidelberg
SKU: 103813309
Price: 30.83 EUR
Availability: OnlineOnly

(Sprache: Englisch)

Autor: Jie Xiao

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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. TOC:Fundamentel Material.- Composite Embedding.- Series Expansions.- Modified Carleson Measures.- Inner-Outer Structure.- Pseudo-holomorphic Extension.- Representation via /bar/partial-equation.- Dyadic Localization.- References.- Index.