Convergence and Summability of Fourier Transforms and Hardy Spaces

Description

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike. Front Matter ....Pages i-xxii Front Matter ....Pages 1-1 One-Dimensional Hardy Spaces (Ferenc Weisz)....Pages 3-70 One-Dimensional Fourier Transforms (Ferenc Weisz)....Pages 71-133 Front Matter ....Pages 135-135 Multi-Dimensional Hardy Spaces (Ferenc Weisz)....Pages 137-202 Multi-Dimensional Fourier Transforms (Ferenc Weisz)....Pages 203-227 ℓq-Summability of Multi-Dimensional Fourier Transforms (Ferenc Weisz)....Pages 229-382 Rectangular Summability of Multi-Dimensional Fourier Transforms (Ferenc Weisz)....Pages 383-411 Back Matter ....Pages 413-435