Holomorphic Q classes / Jie Xiao.

By: Xiao, Jie, 1963-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1767.Publisher: Berlin ; New York : Springer, ©2001Description: 1 online resource (viii, 112 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540454342; 3540454349Subject(s): Holomorphic functions | Holomorphic functionsGenre/Form: Electronic books. Additional physical formats: Print version:: Holomorphic Q classes.DDC classification: 510 s | 515/.9 LOC classification: QA3 | .L28 no. 1767 | QA331.7Online resources: Click here to access online
Contents:
Fundamentel Material -- Composite Embedding -- Series Expansions -- Modified Carleson Measures -- Inner-Outer Structure -- Pseudo-holomorphic Extension -- Representation via /bar/partial-equation -- Dyadic Localization -- References -- Index.
Summary: 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.
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Includes bibliographical references (pages 105-110) and index.

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

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.

English.

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