Bochner-Riesz means on euclidean spaces / Shanzhen Lu, Dunyan Yan.

By:

Lu, Shanzhen, 1939- [author.]

Contributor(s):

Yan, Dunyan [author.]

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9789814458771
9814458775

Subject(s):

Genre/Form:

Additional physical formats: Print version:: Bochner-Riesz means on Euclidean spaces.DDC classification:

515.2433 23

LOC classification:

QA404 .L8 2013eb

Online resources:

Click here to access online

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.

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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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.

Includes bibliographical references (pages 367-374) and index.

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.

Print version record.

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