Maximal averages over surfaces

Advances in Mathematics

Volumn 132, Issue 1, 1997, Pages 46-119

  Iosevich, A ^a   Sawyer, E ^b,c  

^a WRIGHT STATE UNIVERSITY   (United States)

^b MCMASTER UNIVERSITY   (Canada)

^c INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031539481     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1997.1678     Document Type: Article

References (24)

1. Bourgain J. Averages in the plane over convex curves and maximal operators. J. Analyse Math. 47:1986;69-85.
2. Bruna J., Nagel A., Wainger S. Convex hypersurfaces and Fourier transform. Ann. of Math. 127:1988;333-365.
3. Cowling M., Mauceri G. Inequalities for some maximal functions. Trans. Amer. Math. Soc. 296:1986;341-365.
4. Cowling M., Mauceri G. Oscillatory integrals and Fourier transforms of the surface carried measures. Trans. Amer. Math. Soc. 304:1987;53-68.
5. M. de Guzmán, Singular Integral Operators with Generalized Homogeneity.
6. Fabes E. B., Riviere N. M. Singular integrals with mixed homogeneity. Studia Math. 27:1966;19-38.
7. Guan P., Sawyer E. Regularity estimates for the oblique derivative problem. Ann. Math. 137:1993;1-71.
8. Greenleaf A. Principal curvature in harmonic analysis. Indiana Math. J. 30:1981;519-537.
9. A. Iosevich, 1993, Maximal Operators Associated to Families of Flat Curves and Hypersurfaces, UCLA.
10. A. Iosevich, Maximal operators associated to families of flat curves in the plane, Duke Math. J.
11. Iosevich A., Sawyer E. Oscillatory integrals and maximal averages over homogeneous surfaces. Duke Math. J. 82:1996;103-141.
12. qestimates for a class of averaging operators. Ann. Inst. Fourier. 46:1996;1359-1384.
13. n.
14. Nagel A., Seeger A., Wainger S. Averages over convex hypersurfaces. Am. J. Math. 115:1993;903-927.
15. Riviere N. M. On singular integrals. Bull. Amer. Math. Soc. 75:1969;843-847.
16. Ricci F., Stein E. M. Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds. J. Funct. Anal. 86:1989;360-389.
17. Schulz H. Convex hypersurfaces of finite type and the asymptotics of their Fourier transforms. Indiana Univ. Math. J. 40:1991;1267-1275.
18. Seeger A., Sogge C. D., Stein E. M. Regularity properties of Fourier integral operators. Ann. Math. 133:1991;231-251.
19. Sogge C. D. Fourier Integrals in Classical Analysis. 1991;Oxford Univ. Press, Oxford.
20. C. D. Sogge, Maximal operators associated to hypersurfaces with one non-vanishing principal curvature.
21. n. Invent. Math. 82:1985;543-556.
22. Stein E. M. Beijing Lectures in Harmonic Analysis. 1986;Princeton Univ. Press, Princeton.
23. Stein E. M. Maximal functions: spherical means. Proc. Natl. Acad. Sci. 73:1976;2174-2175.
24. Stein E. M. Harmonic Analysis. 1993;Princeton Univ. Press, Princeton.