References
J. Bourgain,Averages in the plane over convex curves and maximal operators, J. Analyse Math.47 (1986), 69–85.
J. Bruna, A. Nagel and S. Wainger,Convex hypersurfaces and Fourier transform, Ann. of Math. (2)127 (1988), 333–365.
D. Catlin,Boundary invariants of pseudoconvex domains, Ann. of Math. (2)120 (1984), 529–586.
M. Christ,Hilbert transforms along curves, I. Nilpotent groups, Ann. of Math. (2)122 (1985), 575–596.
M. Christ,Endpoint bounds for singular fractional integral operators, preprint 1988.
M. Christ,Failure of an endpoint estimate for integrals along curves, inFourier Analysis and Partial Differential Equations (J. Garcia-Cuerva, E. Hernandez, F. Soria and J. L. Torrea, eds.), CRC Press, Boca Raton, 1995.
M. Cowling and G. Mauceri,Inequalities for some maximal functions II, Trans. Amer. Math. Soc.296 (1986), 341–365.
M. Cowling and G. Mauceri,Oscillatory integrals and Fourier transforms of surface carried measures, Trans. Amer. Math. Soc.,304 (1987), 53–68.
M. Cowling, S. Disney, G. Mauceri and D. Müller,Dam** oscillatory integrals, Invent. Math.101 (1990), 237–260.
E. Ferreyra, T. Godoy and M. Urciuolo,Endpoint bounds for convolution operators with singular measures, Colloq. Math.76 (1998), 35–47.
A. Greenleaf,Principal curvature in harmonic analysis, Indiana Univ. Math. J.,30 (1981), 519–537.
A. Iosevich,Maximal operators associated to families of flat curves in the plane Duke Math. J.76 (1994), 633–644.
A. Iosevich and E. Sawyer,Oscillatory integrals and maximal averages over homogeneous surfaces, Duke Math. J.82 (1996), 103–141.
A. Iosevich and E. Sawyer,Maximal averages over surfaces, Adv. Math.132 (1997), 46–119.
A. Iosevich and E. Sawyer,Sharp L p→Lq estimates for a class of averaging operators, Ann. Inst. Fourier (Grenoble)46 (1993), 903–927.
S. H. Lee,Convolution operators with singular measures preprint.
W. Littman,L p-Lq -estimates for singular integral operators, Proc. Symp. Pure Appl. Math.23 (1973), 479–481.
A. Nagel, A. Seeger and S. Wainger,Averages over convex hypersurfaces, Amer. J. Math.115 (1993), 903–927.
F. Ricci and E. M. Stein,Harmonic analysis on nilpotent groups and singular integrals I. Oscillatory integrals, J. Funct. Anal.73 (1987), 179–194.
H. Schulz,Convex hypersurfaces of finite type and the asymptotics of their Fourier transforms, Indiana Univ. Math. J.40, (1991), 1267–1275.
C. D. Sogge and E. M. Stein, Averages of functions over hypersurfaces inR d, Invent. Math.82 (1985), 543–556.
E. M. Stein,Maximal functions: Spherical means, Proc. Nat. Acad. Sci. U.S.A.,73 (1976), 2174–2175
E. M. Stein,Harmonic Analysis, Princeton University Press, 1993.
E. M. Stein and S. Wainger,Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc.84 (1978), 1239–1295.
R. Strichartz,Convolutions with kernels having singularities on a sphere, Trans. Amer. Math. Soc.148 (1970), 461–471.
J. Yu,Multitypes of convex domains, Indiana Univ. Math. J.41 (1992), 837–849.
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Research supported in part by NSF grants.
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Iosevich, A., Sawyer, E. & Seeger, A. On averaging operators associated with convex hypersurfaces of finite type. J. Anal. Math. 79, 159–187 (1999). https://doi.org/10.1007/BF02788239
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DOI: https://doi.org/10.1007/BF02788239