Sharp L p -L q estimates for a class of averaging operators
Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1359-1384.

On obtient des estimations L p -L q pour des opérateurs maximaux associés à des hypersurfaces de R n qui sont des graphes de fonctions homogènes. On en déduit un théorème de régularité pour les solutions d’une certaine équation aux dérivées partielles linéaire.

Sharp L p -L q estimates are obtained for averaging operators associated to hypersurfaces in R n given as graphs of homogeneous functions. An application to the regularity of an initial value problem is given.

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     author = {Iosevich, Alex and Sawyer, Eric},
     title = {Sharp $L^p-L^q$ estimates for a class of averaging operators},
     journal = {Annales de l'Institut Fourier},
     pages = {1359--1384},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {46},
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     year = {1996},
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Iosevich, Alex; Sawyer, Eric. Sharp $L^p-L^q$ estimates for a class of averaging operators. Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1359-1384. doi : 10.5802/aif.1553. https://aif.centre-mersenne.org/articles/10.5802/aif.1553/

[Io1] A. Iosevich, Maximal operators associated to families of flat curves in the plane, Duke Math. J., 76 (1994), 633-644. | MR | Zbl

[Io2] A. Iosevich, Averages over homogeneous hypersurfaces in R3, to appear in Forum Mathematicum, January (1996). | MR | Zbl

[IoSa] A. Iosevich and E. Sawyer, Oscillatory integrals and maximal averages over homogeneous surfaces, Duke Math. J., 82 (1996), 1-39. | MR | Zbl

[KPV] C. Kenig, G. Ponce, and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Math. J., 40 (1991), 33-69. | MR | Zbl

[Litt] W. Littman, Lp — Lq estimates for singular integral operators, Proc. Symp. Pure Math., 23 (1973), 479-481. | MR | Zbl

[RiSt] F. Ricci and E.M. Stein, Harmonic analysis on nilpotent groups and singular integrals III, Jour. Funct. Anal., 86 (1989), 360-389. | MR | Zbl

[So] C.D. Sogge, Fourier integrals in classical analysis, Cambridge Univ. Press, 1993. | MR | Zbl

[St1] E.M. Stein, Lp boundedness of certain convolution operators, Bull. Amer. Math. Soc., 77 (1971), 404-405. | MR | Zbl

[St2] E.M. Stein, Harmonic Analysis, Princeton University Press, 1993. | Zbl

[Str] R. Strichartz, Convolutions with kernels having singularities on the sphere, Trans. Amer. Math. Soc., 148 (1970), 461-471. | MR | Zbl

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