no. 5
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.

@article{AIF_1996__46_5_1359_0,
     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},
     number = {5},
     year = {1996},
     doi = {10.5802/aif.1553},
     zbl = {0898.42003},
     mrnumber = {98a:42008},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1553/}
}
TY  - JOUR
AU  - Iosevich, Alex
AU  - Sawyer, Eric
TI  - Sharp $L^p-L^q$ estimates for a class of averaging operators
JO  - Annales de l'Institut Fourier
PY  - 1996
SP  - 1359
EP  - 1384
VL  - 46
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1553/
DO  - 10.5802/aif.1553
LA  - en
ID  - AIF_1996__46_5_1359_0
ER  - 
%0 Journal Article
%A Iosevich, Alex
%A Sawyer, Eric
%T Sharp $L^p-L^q$ estimates for a class of averaging operators
%J Annales de l'Institut Fourier
%D 1996
%P 1359-1384
%V 46
%N 5
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1553/
%R 10.5802/aif.1553
%G en
%F AIF_1996__46_5_1359_0
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

Cité par Sources :