Historically, the theory of Hilbert spaces originated from David Hilbert's (1862–1943) work
on quadratic forms in infinitely many variables with their applications to integral equations …

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 …

A concise yet elementary introduction to measure and integration theory, which are vital in
many areas of mathematics, including analysis, probability, mathematical physics and …

This note is a very basic introduction to wavelets. It starts with an orthogonal basis of
piecewise constant functions, constructed by dilation and translation. The" wavelet …

This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks
that aim to present, in an integrated manner, the core areas of analysis. Beginning with the …

In this paper we discuss and prove an analogy of the Carleson–Hunt theorem with respect to
Vilenkin systems. In particular, we use the theory of martingales and give a new and shorter …

The history of martingale theory goes back to the early fifties when Doob [57] pointed out the
connection between martingales and analytic functions. On the basis of Burkholder's …

We study the interplay between unconditional decompositions and the R-boundedness of
collections of operators. In particular, we get several multiplier results of Marcinkiewicz type …

This book is concerned with applications of functional analysis and complex analysis to
problems of interpolation in spaces of analytic functions. The problems we look at are those …

Spectral techniques facilitate the design and testing of today's increasingly complex digital
devices There is heightened interest in spectral techniques for the design of digital devices …