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Uniform Weak (1,1) Bounds for Oscillatory Singular Integrals

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Book cover Harmonic Analysis in China

Part of the book series: Mathematics and Its Applications ((MAIA,volume 327))

Abstract

Oscillatory singular integrals arise in many problems in harmonic analysis. Their boundedness properties have been studied quite extensively (see, for example, Stein [13]). In this paper we shall establish a uniform L 1 → L 1,∞ estimate for certain oscillatory singular integral operators with smooth phase functions of finite type. Such estimate has been known previously for operators with real-analytic phases only.

Supported in part by a grant from the National Science Foundation.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Yibiao Pan

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  1. Yibiao Pan
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, China

    Minde Cheng

  2. Department of Mathematics, Zhongshan University, Guangzhou, China

    Dong-gao Deng

  3. Department of Mathematics, University of Science and Technology, Hefei, China

    Sheng Gong

  4. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon,Hong Kong, China

    Chung-Chun Yang

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© 1995 Springer Science+Business Media Dordrecht

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Pan, Y. (1995). Uniform Weak (1,1) Bounds for Oscillatory Singular Integrals. In: Cheng, M., Deng, Dg., Gong, S., Yang, CC. (eds) Harmonic Analysis in China. Mathematics and Its Applications, vol 327. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0141-7_12

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  • DOI: https://doi.org/10.1007/978-94-011-0141-7_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4064-8

  • Online ISBN: 978-94-011-0141-7

  • eBook Packages: Springer Book Archive

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