Propagation of singularities and maximal functions in the plane

Christopher D. Sogge

doi:10.1007/bf01245080

journal article Dec 01, 1991

Propagation of singularities and maximal functions in the plane

Christopher D. Sogge

Inventiones mathematicae Vol. 104 No. 1 pp. 349-376 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf01245080

Topics

No keywords indexed for this article. Browse by subject →

References

24

[1]

Besse, A.L.: Manifolds all of whose geodesics are closed. Berlin Heidelberg New York: Springer 1978 10.1007/978-3-642-61876-5

[2]

Bourgain, J.: Averages in the plane over convex curves and maximal operators. J. Analyse Math.47, 69–85 (1986) 10.1007/bf02792533

[3]

Carbery, A.: The boundedness of the maximal Bochner-Riesz operator onL 4(ℝ2). Duke Math. J.50, 409–416 (1983) 10.1215/s0012-7094-83-05018-4

[4]

Carleson, L., Sjölin, P.: Oscillatory integrals and a multiplier problem for the disk. Studia Math.44, 287–299 (1972) 10.4064/sm-44-3-287-299

[5]

Constantin, P., Saut, J.: Local smoothing properties of dispersive equations. J. Amer. Math. Soc.1, 431–439 (1988) 10.1090/s0894-0347-1988-0928265-0

[6]

Falconer, K.J.: The geometry of fractal sets. Cambridge: Cambridge Univ. Pres 1985 10.1017/cbo9780511623738

[7]

Fourier integral operators. I

Lars Hörmander

Acta Mathematica 1971 10.1007/bf02392052

[8]

Hörmander, L.: The spectral function of an elliptic operator. Acta Math.88, 341–370 (1968)

[9]

Hörmander, L.: The analysis of linear partial differential operators III, IV. Berlin Heidelberg New York: Springer 1985

[10]

Journé, J.-L., Soffer, A., Sogge, C.D.: Decay estimates for Schrödinger operators. Comm. Pure Appl. Math. (to appear) 10.1002/cpa.3160440504

[11]

Kaneko, M., Sunouchi, G.: On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions. Tôhoku Math. J.37, 343–365 (1985) 10.2748/tmj/1178228647

[12]

Kato, T.: On the Cauchy problem for the (generalized) Kortveg-de Vries equation. In: Studies in Applied Math., pp. 9–23, Academic Press 1986

[13]

Peral, J.:L p estimates for the wave equation. J. Funct. Anal.36, 114–145 (1980) 10.1016/0022-1236(80)90110-x

[14]

Phong, D.H., Stein, E.M.: Hilbert integrals, singular integrals and Radon transforms I. Acta Math.157, 99–157 (1986) 10.1007/bf02392592

[15]

Seeger, A., Sogge, C.D., Stein, E.M.: Regularity properties of Fourier integral operators, Ann. Math. (to appear) 10.2307/2944346

[16]

Sjölin, P.: Regularity of solutions to the Schrödinger equation. Duke Math. J.55, 699–715 (1987) 10.1215/s0012-7094-87-05535-9

[17]

Sogge, C.D., Stein, E.M.: Averages over hypersufaces: smoothness of generalized Radon transforms. J. Anal. Math.54, 165–188 (1990) 10.1007/bf02796147

[18]

Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton: Princeton Univ. Press 1970

[19]

Stein, E.M.: Maximal functions: spherical means. Proc. Nat. Acad. Sci.73, 2174–2175 (1976) 10.1073/pnas.73.7.2174

[20]

Stein, E.M.: Oscillatory integrals in Fourier analysis. In: Beijing lectures in harmonic analysis, pp. 307–356. Princeton: Princeton Univ. Press 1986

[21]

Stein, E.M., Wainger, S.: Problems in harmonic analysis related to curvature. Bull. Amer. Math. Soc.84, 1239–1295 (1978) 10.1090/s0002-9904-1978-14554-6

[22]

Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton: Princeton Univ. Press 1971

[23]

Vega, L.: Schrödinger equations: pointwise convergence to the initial data. Proc. Amer. Math. Soc.102, 874–878 (1988)

[24]

Wilder, J.B.: The non-Euclidean Kakeya problem. In: Proceedings of the 25th summer meeting of the Canadian Mathematical Congress. 1971, pp. 603–607

Metrics

71

Citations

24

References

Details

Published: Dec 01, 1991
Vol/Issue: 104(1)
Pages: 349-376
License: View

Authors

C

Christopher D. Sogge

Cite This Article

Christopher D. Sogge (1991). Propagation of singularities and maximal functions in the plane. Inventiones mathematicae, 104(1), 349-376. https://doi.org/10.1007/bf01245080

Propagation of singularities and maximal functions in the plane

You May Also Like