Skip to main content

Young’s Inequality Sharpened

  • Conference paper
  • First Online:
Geometric Aspects of Harmonic Analysis

Part of the book series: Springer INdAM Series ((SINDAMS,volume 45))

Abstract

A quantitative stability result with an optimal exponent is established, concerning near-maximizers for Young’s convolution inequality for Euclidean groups.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    These are not Fourier coefficients.

References

  1. Beckner, W.: Inequalities in Fourier analysis. Ann. Math. (2) 102(1), 159–182 (1975)

    Google Scholar 

  2. Bennett, J., Carbery, A., Christ, M., Tao, T.: The Brascamp-Lieb inequalities: finiteness, structure and extremals. Geom. Funct. Anal. 17(5), 1343–1415 (2008)

    Article  MathSciNet  Google Scholar 

  3. Bianchi, G., Egnell, H.: A note on the Sobolev inequality. J. Funct. Anal. 100(1), 18–24 (1991)

    Article  MathSciNet  Google Scholar 

  4. Brascamp, H.J., Lieb, E.H.: Best constants in Young’s inequality, its converse, and its generalization to more than three functions. Adv. Math. 20(2), 151–173 (1976)

    Article  MathSciNet  Google Scholar 

  5. Carlen, E.A., Lieb, E.H., Loss, M.: A sharp analog of Young’s inequality on S N and related entropy inequalities. J. Geom. Anal. 14(3), 487–520 (2004)

    Article  MathSciNet  Google Scholar 

  6. Christ, M.: Near equality in the Riesz-Sobolev inequality. Acta Math. Sin. (Engl. Ser.) 35(6), 783–814 (2019)

    Google Scholar 

  7. Christ, M.: Near-extremizers of Young’s inequality for Euclidean groups. Rev. Mat. Iberoam. 35(7), 1925–1972 (2019)

    Article  MathSciNet  Google Scholar 

  8. Christ, M.: A sharpened Hausdorff–Young inequality (2014). Preprint, math.CA arXiv:1406.1210

    Google Scholar 

  9. Christ, M.: A sharpened Riesz-Sobolev inequality (2017). Preprint, math.CA arXiv:1706.02007

    Google Scholar 

  10. Christ, M.: On Young’s inequality for Heisenberg groups. In: Geometric Aspects of Harmonic Analysis. Springer, Berlin (2021)

    Google Scholar 

  11. O’Neill, K.: A quantitative stability theorem for convolution on the Heisenberg group (2019). Preprint, math.CA arXiv:1907.11986

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Christ .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Christ, M. (2021). Young’s Inequality Sharpened. In: Ciatti, P., Martini, A. (eds) Geometric Aspects of Harmonic Analysis. Springer INdAM Series, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-030-72058-2_7

Download citation

Publish with us

Policies and ethics