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Harmonic Measure
During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.
Bounded Analytic Functions
This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available.
Bounded Analytic Functions
Bounded Analytic Functions
Harmonic Measure
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Applications of Harmonic Measure
This monograph illustrates how elementary harmonic measure arguments have broad applications. The author presents some recent results on harmonic measure and applications of harmonic measure estimates to problems in analysis and spectral theory. Most of the results included are not available in any other book. The treatment is elementary in that Brownian motion is not used--the introduction gives all the background needed for following the text. Chapters cover length sums, level curves of conformal mappings, interpolating sequences, nontangential limit sets, Makarov's theorems, and periodic spectra of Hill's equation.
Harmonic Measure
An introduction to harmonic measure on plane domains and careful discussion of the work of Makarov, Carleson, Jones and others.
