Holomorphic Q Classes

ISBN-13: 9783540426257 / Angielski / Miękka / 2001 / 104 str.

Jie Xiao; J. Xiao

Opis

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

Spis treści

1. Fundamental Material 1.1 Introduction 1.2 Inclusion 1.3 Image Area Notes 2. Composite Embedding 2.1 Existence of BiBloch-Type Mappings 2.2 Boundedness and Compactness 2.3 Geometric Characterizations Notes 3. Series Expansion 3.1 Power Series 3.2 Partial Sums 3.3 Nonnegative Coefficients 3.4 Random Series Notes 4. Modified Carleson Measures 4.1 An Integral Form 4.2 Relating to Mean Lipschitz Spaces 4.3 Comparison with Besov Spaces 4.4 Mean Growth Notes 5. Inner-Outer Structure 5.1 Singular Facturs 5.2 Blaschke Products 5.3 Outer Functions 5.4 Canonical Factorization Notes 6. Pseudo-holomorphic Extension 6.1 Boundary Value Behavior 6.2 Weight Condition 6.3 Pseudo-holomorphic Continuation 6.4 K-property Notes 7. Representation via /bar/partial-equation 7.1 Harmonic Extension 7.2 /bar/partial-estimates 7.3 Fefferman-Stein Type Decomposition 7.4 Corona Data and Solutions 7.5 Interpolating Sequences Notes 8. Dyadic Localization 8.1 Square Mean Oscillation 8.2 Dyadic Model 8.3 Wavelets Notes References Index