Sharp L p - L q estimates for a class of averaging operators

Alex Iosevich; Eric Sawyer

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 5, page 1359-1384
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Iosevich, Alex, and Sawyer, Eric. "Sharp $L^p-L^q$ estimates for a class of averaging operators." Annales de l'institut Fourier 46.5 (1996): 1359-1384. <http://eudml.org/doc/75217>.

@article{Iosevich1996,
abstract = {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.},
author = {Iosevich, Alex, Sawyer, Eric},
journal = {Annales de l'institut Fourier},
keywords = {averaging operators; hypersurfaces; homogeneous functions; norm inequality},
language = {eng},
number = {5},
pages = {1359-1384},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sharp $L^p-L^q$ estimates for a class of averaging operators},
url = {http://eudml.org/doc/75217},
volume = {46},
year = {1996},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 5
SP - 1359
EP - 1384
AB - 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.
LA - eng
KW - averaging operators; hypersurfaces; homogeneous functions; norm inequality
UR - http://eudml.org/doc/75217
ER -

References

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  1. [Io1] A. IOSEVICH, Maximal operators associated to families of flat curves in the plane, Duke Math. J., 76 (1994), 633-644. Zbl0827.42010MR95k:42028
  2. [Io2] A. IOSEVICH, Averages over homogeneous hypersurfaces in R3, to appear in Forum Mathematicum, January (1996). Zbl0862.42012MR97m:42015
  3. [IoSa] A. IOSEVICH and E. SAWYER, Oscillatory integrals and maximal averages over homogeneous surfaces, Duke Math. J., 82 (1996), 1-39. Zbl0898.42004MR97f:42035
  4. [KPV] C. KENIG, G. PONCE, and L. VEGA, Oscillatory integrals and regularity of dispersive equations, Indiana Math. J., 40 (1991), 33-69. Zbl0738.35022MR92d:35081
  5. [Litt] W. LITTMAN, Lp — Lq estimates for singular integral operators, Proc. Symp. Pure Math., 23 (1973), 479-481. Zbl0263.44006MR50 #10909
  6. [RiSt] F. RICCI and E.M. STEIN, Harmonic analysis on nilpotent groups and singular integrals III, Jour. Funct. Anal., 86 (1989), 360-389. Zbl0684.22006MR90m:22027
  7. [So] C.D. SOGGE, Fourier integrals in classical analysis, Cambridge Univ. Press, 1993. Zbl0783.35001MR94c:35178
  8. [St1] E.M. STEIN, Lp boundedness of certain convolution operators, Bull. Amer. Math. Soc., 77 (1971), 404-405. Zbl0217.44503MR43 #2497
  9. [St2] E.M. STEIN, Harmonic Analysis, Princeton University Press, 1993. Zbl0821.42001
  10. [Str] R. STRICHARTZ, Convolutions with kernels having singularities on the sphere, Trans. Amer. Math. Soc., 148 (1970), 461-471. Zbl0199.17502MR41 #876

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