This book deals with the theory of one- and two-parameter
martingale Hardy spaces and their use in Fourier analysis, and
gives a summary of the latest results in this field. A method that
can be applied for both one- and two-parameter cases, the so-called
atomic decomposition method, is improved and provides a new and
common construction of the theory of one- and two-parameter
martingale Hardy spaces. A new proof of Carleson's convergence
result using martingale methods for Fourier series is given with
martingale methods. The book is accessible to readers familiar with
the fundamentals of probability theory and analysis. It is intended
for researchers and graduate students interested in martingale
theory, Fourier analysis and in the relation between them.
General
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