The Journal of Geometric Analysis

, Volume 9, Issue 4, pp 583–605

Classes of singular integral operators along variable lines

  • Anthony Carbery
  • Andreas Seeger
  • Stephen Wainger
  • James Wright
Article

DOI: 10.1007/BF02921974

Cite this article as:
Carbery, A., Seeger, A., Wainger, S. et al. J Geom Anal (1999) 9: 583. doi:10.1007/BF02921974

Abstract

We prove estimates for classes of singular integral operators along variable lines in the plane, for which the usual assumption of nondegenerate rotational curvature may not be satisfied. The main Lp estimates are proved by interpolating L2 bounds with suitable bounds in Hardy spaces on product domains. The L2 bounds are derived by almost-orthogonality arguments. In an appendix we derive an estimate for the Hilbert transform along the radial vector field and prove an interpolation lemma related to restricted weak type inequalities.

Math Subject Classifications

42B2035S3046B70

Key Words and Phrases

singular integrals along variable linesalmost orthogonality argumentsCalderón-Zygmund theory on product spacesradial Hilbert transformrestricted weak type inequalities

Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

  • Anthony Carbery
    • 1
    • 2
  • Andreas Seeger
    • 1
    • 2
  • Stephen Wainger
    • 1
    • 2
  • James Wright
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of EdinburghEdinburghUK
  2. 2.Department of MathematicsUniversity of WisconsinMadison
  3. 3.School of MathematicsUniversity of New South WalesSydneyAustralia