Holomorphic Q classes / Jie Xiao.

Format:

Book

Author/Creator:

Xiao, Jie, 1963-

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1767.

Lecture notes in mathematics, 0075-8434 ; 1767

Language:

English

Subjects (All):

Holomorphic functions.

Physical Description:

viii, 112 pages ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, [2001]

Summary:

PMThe 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 example

Notes:

Includes bibliographical references (pages [105]-110) and index.

ISBN:

3540426256

OCLC:

47996314