Table of contents
About this book
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.
Fejér summability fourier analysis hardy spaces Lebesgue points strong summability harmonic analysis atomic decomposition Hardy-Littlewood maximal function multi-dimensional summability circular, triangular and cubic summability theta-summability
- DOI https://doi.org/10.1007/978-3-319-56814-0
- Copyright Information Springer International Publishing AG 2017
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-319-56813-3
- Online ISBN 978-3-319-56814-0
- Series Print ISSN 2296-5009
- Series Online ISSN 2296-5017
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