Classes of singular integral operators along variable lines

Journal of Geometric Analysis

Volumn 9, Issue 4, 1999, Pages 583-605

  Carbery, Anthony ^b   Seeger, Andreas ^b   Wainger, Stephen ^b   Wright, James ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b NONE

Author keywords

Almost orthogonality arguments; Calder n Zygmund theory on product spaces; Radial Hilbert transform; Restricted weak type inequalities; Singular integrals along variable lines

Indexed keywords

EID: 29244464836     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02921974     Document Type: Article

References (26)

1. Bergh, J. and Löfström, J. Interpolation Spaces. Grundlehren der mathematischen Wissenschaften, 223, Springer-Verlag, Berlin, 1976.
2. Bourgain, J. Estimations de certaines fonctions maximales, C. R. Acad. Sc. Paris, 310, 499-502, (1985).
3. Bourgain, J. A remark on the maximal function associated to an analytic vector field, Analysis at Urbana. Berkson, E., Peck, T., and Uhl, J., Eds., Cambridge University Press, 111-132, 1989.
4. Carbery, A., Hernandez, E., and Soria, F. Estimates for the Kakeya maximal operator on radial functions, Proc. ICM-90 Satellite Conference on Harmonic Analysis, Igari, S., Ed., Springer-Verlag, Berlin, 41-50, 1991.
5. p variants of multiparameter Calderón-Zygmund theory, Trans. Am. Math. Soc., 334, 719-747, (1992).
6. Carbery, A., Wainger, S., and Wright, J. Hilbert transforms and maximal functions along flat variable plane curves, J. Fourier Anal. Appl., Kahane special issue, 119-139, (1995).
7. Carbery, A., Wainger, S., and Wright, J. A variant of the notion of a space of homogeneous type, J. Funct. Anal., 132, 119-140, (1995).
8. Carleson, L. On convergence and growth of partial sums of Fourier series, Acta Math., 116, 135-157, (1966).
9. Chang, S.Y.A. and Fefferman, R. The Calderón-Zygmund decomposition on product domains, Am. J. Math., 104, 445-468, (1982).
10. Christ, M. Hilbert transforms along curves III, Rotational curvature, unpublished manuscript, 1986.
11. Christ, M., Nagel, A., Stein, E.M., and Wainger, S. Singular and maximal Radon transforms, in preparation.
12. Fefferman, C. and Stein, E.M. Some maximal inequalities, Am. J. Math., 93, 107-115, (1971).
13. Fefferman, R. Harmonic analysis on product spaces, Ann. Math., 126, 109-130, (1987).
14. b, complex and analysis on the Heisenberg group, Comm. Pure Appl. Math., 27, 429-522, (1974).
15. Greenleaf, A. and Uhlmann, G. Estimates for singular Radon transforms and pseudo-differential operators with singular symbols, J. Funct. Anal., 89, 202-232, (1990).
16. Hunt, R.A. On the convergence of Fourier series, Proceedings of the S. I. U. Conference on Orthogonal Expansions. Southern Illinois University Press, Carbondale, IL, 235-255, 1968.
17. Journé, J.L. Calderón-Zygmund operators on product spaces. Rev. Mat. Iberoamericana, 1, 55-91, (1985).
18. Nagel, A., Stein, E.M., and Wainger, S. Hilbert transforms and maximal functions related to variable curves, Harmonic Analysis in Euclidean Spaces, I, Wainger, S. and Weiss, G., Eds., Proc. Symp. Pure Math., 35, Am. Math. Society.
19. Phong, D.H. and Stein, E.M. Hilbert integrals, singular integrals and Radon transforms I, Acta Math., 157, 99-157, (1986).
20. Phong, D.H. and Stein, E.M. Singular Radon transforms and oscillatory integrals, Duke Math. J., 58, 347-369, (1989).
21. Phong, D.H. and Stein, E.M. Radon transforms and torsion, Intl. Math. Res. Not., appeared as an appendix in Duke Math. J., 49-60, (1991).
22. Seeger, A. Degenerate Fourier integral operators in the plane, Duke Math. J., 71, 685-745, (1993).
23. 2 estimates for a class of singular oscillatory integrals, Math. Res. Lett., 1, 65-73, (1994).
24. Stein, E.M. Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993.
25. Stein, E.M. and Wainger, S. Problems in harmonic analysis related to curvature, Bull. Am. Math. Soc., 84, 1239-1295, (1978).
26. Stein, E.M. and Weiss, G. Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, NJ, 1971.