Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T14:57:17.066Z Has data issue: false hasContentIssue false
  • English
  • Français

DOUBLE HILBERT TRANSFORMS ALONG POLYNOMIAL SURFACES IN R3

Published online by Cambridge University Press:  01 September 2008

SANJAY PATEL
SANJAY PATEL*
Affiliation:
Department of Mathematics, School of Sciences, Gujarat University, Navrangpura, Ahmedabad-380009, India e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain a necessary and sufficient condition on a polynomial P(s, t) so that the (global) double Hilbert transforms along polynomial surfaces (s, t, P(s, t)) in R3 are bounded on Lp for 1 < p < ∞.

Keywords

42B20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 395 - 428
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Carbery, A., Christ, M. and Wright, J., Multidimensional van der Corput and sublevel set estimates, J. Amer. Math. Soc. 12 (4) (1999), 981–1015.CrossRefGoogle Scholar
2.Carbery, A., Wainger, S. and Wright, J., Double Hilbert transforms along polynomial surfaces in R3, Duke. Math. J. 101 (3) (2000), 499–513.CrossRefGoogle Scholar
3.Duoandikoetxea, J. and Rubio de Francia, J. L., Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541–561.CrossRefGoogle Scholar
4.Ricci, F. and Stein, E. M., Multiparameter singular integrals and maximal functions, Ann. Inst. Fourier (Grenoble) 42 (1992), 637–670.CrossRefGoogle Scholar
5.Stein, E. M., Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals (Princeton University Press, Princeton, NJ, 1993).Google Scholar