# Lp-bounds for spherical maximal operators on Zn.

Revista Matemática Iberoamericana (1997)

- Volume: 13, Issue: 2, page 307-317
- ISSN: 0213-2230

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topMagyar, Akos. "Lp-bounds for spherical maximal operators on Zn.." Revista Matemática Iberoamericana 13.2 (1997): 307-317. <http://eudml.org/doc/39542>.

@article{Magyar1997,

abstract = {We prove analogue statements of the spherical maximal theorem of E. M. Stein, for the lattice points Zn. We decompose the discrete spherical measures as an integral of Gaussian kernels st,ε(x) = e2πi|x|2(t + iε). By using Minkowski's integral inequality it is enough to prove Lp-bounds for the corresponding convolution operators. The proof is then based on L2-estimates by analysing the Fourier transforms ^st,ε(ξ), which can be handled by making use of the circle method for exponential sums. As a corollary one obtains some regularity of the distribution of lattice points on small spherical caps.},

author = {Magyar, Akos},

journal = {Revista Matemática Iberoamericana},

keywords = {Operadores integrales; Operadores maximales; Espacios LP; Integrales singulares; spherical maximal operators; -bounds; Fourier transforms; distribution of lattice points on small spherical caps},

language = {eng},

number = {2},

pages = {307-317},

title = {Lp-bounds for spherical maximal operators on Zn.},

url = {http://eudml.org/doc/39542},

volume = {13},

year = {1997},

}

TY - JOUR

AU - Magyar, Akos

TI - Lp-bounds for spherical maximal operators on Zn.

JO - Revista Matemática Iberoamericana

PY - 1997

VL - 13

IS - 2

SP - 307

EP - 317

AB - We prove analogue statements of the spherical maximal theorem of E. M. Stein, for the lattice points Zn. We decompose the discrete spherical measures as an integral of Gaussian kernels st,ε(x) = e2πi|x|2(t + iε). By using Minkowski's integral inequality it is enough to prove Lp-bounds for the corresponding convolution operators. The proof is then based on L2-estimates by analysing the Fourier transforms ^st,ε(ξ), which can be handled by making use of the circle method for exponential sums. As a corollary one obtains some regularity of the distribution of lattice points on small spherical caps.

LA - eng

KW - Operadores integrales; Operadores maximales; Espacios LP; Integrales singulares; spherical maximal operators; -bounds; Fourier transforms; distribution of lattice points on small spherical caps

UR - http://eudml.org/doc/39542

ER -

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