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Bochner-Riesz means on euclidean spaces

Author: Shanzhen Lu; Dunyan Yan
Publisher: [Hackensack] New Jersey : World Scientific, [2013] ©2013
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the disc multiplier conjecture, the famous  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lu, Shanzhen, 1939-
Bochner-Riesz means on Euclidean spaces.
Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte Ltd, [2013]
(OCoLC)826997409
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Shanzhen Lu; Dunyan Yan
ISBN: 9789814458771 9814458775
OCLC Number: 861528243
Description: 1 online resource (viii, 376 pages)
Contents: An introduction to multiple Fourier series --
Bochner-Riesz means of multiple Fourier integral --
Bochner-Riesz means of multiple Fourier series --
The conjugate Fourier integral and series.
Responsibility: Shanzhen Lu, Dunyan Yan.

Abstract:

This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the disc multiplier conjecture, the famous Carleson-Sjölin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means of multiple Fourier series, it includes the theory and application of a class of function space generated by blocks, which is closely related to almost everywhere convergence of the Bochner-Riesz means. In addition, the book also introduce some research results on approximation of functions by the Bochner-Riesz means.

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