# Multiple singular integrals and maximal functions along hypersurfaces

Annales de l'institut Fourier (1986)

- Volume: 36, Issue: 4, page 185-206
- ISSN: 0373-0956

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topDuoandikoetxea, Javier. "Multiple singular integrals and maximal functions along hypersurfaces." Annales de l'institut Fourier 36.4 (1986): 185-206. <http://eudml.org/doc/74734>.

@article{Duoandikoetxea1986,

abstract = {Maximal functions written as convolution with a multiparametric family of positive measures, and singular integrals whose kernel is decomposed as a multiple series of measures, are shown to be bounded in $L^ p$, $1< p< \infty $. The proofs are based on the decomposition of the operators according to the size of the Fourier transform of the measures, assuming some regularity at zero and decay at infinity of these Fourier transforms. Applications are given to homogeneous singular integrals in product spaces with size conditions on the kernel and maximal functions and multiple Hilbert transforms along different types of surfaces.},

author = {Duoandikoetxea, Javier},

journal = {Annales de l'institut Fourier},

keywords = {Maximal functions; singular integrals; Hilbert transforms; surfaces},

language = {eng},

number = {4},

pages = {185-206},

publisher = {Association des Annales de l'Institut Fourier},

title = {Multiple singular integrals and maximal functions along hypersurfaces},

url = {http://eudml.org/doc/74734},

volume = {36},

year = {1986},

}

TY - JOUR

AU - Duoandikoetxea, Javier

TI - Multiple singular integrals and maximal functions along hypersurfaces

JO - Annales de l'institut Fourier

PY - 1986

PB - Association des Annales de l'Institut Fourier

VL - 36

IS - 4

SP - 185

EP - 206

AB - Maximal functions written as convolution with a multiparametric family of positive measures, and singular integrals whose kernel is decomposed as a multiple series of measures, are shown to be bounded in $L^ p$, $1< p< \infty $. The proofs are based on the decomposition of the operators according to the size of the Fourier transform of the measures, assuming some regularity at zero and decay at infinity of these Fourier transforms. Applications are given to homogeneous singular integrals in product spaces with size conditions on the kernel and maximal functions and multiple Hilbert transforms along different types of surfaces.

LA - eng

KW - Maximal functions; singular integrals; Hilbert transforms; surfaces

UR - http://eudml.org/doc/74734

ER -

## References

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- [2] H. CARLSSON, P. SJÖGREN, Estimates for maximal functions along hypersurfaces, Univ. of Göteborg, preprint, 1984. Zbl0629.42010
- [3] H. CARLSSON, P. SJÖGREN, J. O. STROMBERG, Multiparameter maximal functions along dilation invariant hypersurfaces, Univ. of Göteborg, preprint, 1984. Zbl0578.42018
- [4] J. DUOANDIKOETXEA, J. L. RUBIO DE FRANCIA, Maximal and singular integral operators via Fourier transform estimates, Invent. Math., 84 (1986), 541-561. Zbl0568.42012MR87f:42046
- [5] R. FEFFERMAN, Singular integrals on product domains, Bull. Amer. Math. Soc., 4 (1981), 195-201. Zbl0466.42007MR83i:42014
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- [8] A. NAGEL, S. WAINGER, L2-boundedness of Hilbert transforms along surfaces and convolution operators homogeneous with respect to a multiple parameter group, Amer. J. Math., 99 (1977), 761-785. Zbl0374.44003MR56 #9192
- [9] J. L. RUBIO DE FRANCIA, Factorization theory and Ap weights, Amer. J. Math., 106 (1984), 533-547. Zbl0558.42012MR86a:47028a
- [10] E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton N.J., 1970. Zbl0207.13501MR44 #7280
- [11] E. M. STEIN, S. WAINGER, Problems in Harmonic Analysis related to curvature, Bull. Amer. Math. Soc., 84 (1978), 1239-1295. Zbl0393.42010MR80k:42023
- [12] R. S. STRICHARTZ, Singular integrals supported in manifolds, Studia Math., 74 (1982), 137-151. Zbl0501.43007MR85c:42019
- [13] J. T. VANCE, Lp-boundedness of the multiple Hilbert transform along a surface, Pacific J. Math., 108 (1983), 221-241. Zbl0462.44001MR85h:44010

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