Abstract
P. Fatou, G. H. Hardy, and F. Riesz were the pioneers in the study of the boundary behavior of holomorphic functions. In 1906, quick on the heels of Lebesgue’s first publications on measure theory, Fatou proved a seminal result about the almost-everywhere boundary limits of bounded, holomorphic functions on the disk. Interestingly, be was able to render the problem as one about convergence of Fourier series, and he solved it in that language.
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© 2006 Birkhäuser Boston
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(2006). The Boundary Behavior of Holomorphic Functions. In: Krantz, S.G. (eds) Geometric Function Theory. Cornerstones. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4440-7_6
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DOI: https://doi.org/10.1007/0-8176-4440-7_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4339-3
Online ISBN: 978-0-8176-4440-6
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