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Holomorphic Q Classes (Lecture Notes in Mathematics) by Jie Xiao (Repost)

Posted on 2011-05-15




Name:Holomorphic Q Classes (Lecture Notes in Mathematics) by Jie Xiao (Repost)
ASIN/ISBN:3540426256
Publisher:Springer
Publish Date:1 edition (November 28, 2001)
Pages:112
File size:1.04 Mb
Publisher: Springer; 1 edition (November 28, 2001)
ISBN: 3540426256
Pages: 112
File Size: 1.04 MB
Other Info: DJVU
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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.

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