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Multilinear singular integral forms of Christ-Journé type

Author: Andreas Seeger, (Mathematics professor); Charles K Smart; Brian Street
Publisher: [Providence, Rhode Island] : American Mathematical Society, 2019. ©2019
Series: Memoirs of the American Mathematical Society, no. 1231.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
We introduce a class of multilinear singular integral forms which generalize the Christ-Journe multilinear forms. The research is partially motivated by an approach to Bressan’s problem on incompressible mixing flows. A key aspect of the theory is that the class of operators is closed under adjoints (i.e. the class of multilinear forms is closed under permutations of the entries). This, together with an  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Andreas Seeger, (Mathematics professor); Charles K Smart; Brian Street
ISBN: 9781470434373 1470434377
OCLC Number: 1081336617
Notes: "January 2019, volume 257, number 1231 (first of 6 numbers)" -- title page.
Description: v, 134 pages ; 26 cm.
Contents: Chapter 1. Introduction --
Chapter 2. Statements of the main results --
Chapter 3. Kernels --
Chapter 4. Adjoints --
Chapter 5. Outline of the proof of boundedness --
Chapter 6. Some auxiliary operators --
Chapter 7. Basic L[raised to the power of 2] estimates --
Chapter 8. Some results from Calderón-Zygmund theory --
Chapter 9. Almost orthogonality --
Chapter 10. Boundedness of Multilinear Singular Forms --
Chapter 11. Interpolation --
Bibliography.
Series Title: Memoirs of the American Mathematical Society, no. 1231.
Responsibility: Andreas Seeger, Charles K. Smart, Brian Street.

Abstract:

We introduce a class of multilinear singular integral forms which generalize the Christ-Journe multilinear forms. The research is partially motivated by an approach to Bressan’s problem on incompressible mixing flows. A key aspect of the theory is that the class of operators is closed under adjoints (i.e. the class of multilinear forms is closed under permutations of the entries). This, together with an interpolation, allows us to reduce the boundedness.

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