Lp-bounds for spherical maximal operators on Zn.

Título inglés Lp-bounds for spherical maximal operators on Zn.
Título español Límites Lp para operadores maximales esféricos sobre Zn.
Autor/es Magyar, Akos
Organización Dep. Math. California Inst. Technol., Pasadena (California), Estados Unidos
Revista 0213-2230
Publicación 1997, 13 (2): 307-317, 4 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120201
Palabras clave español Operadores integrales ; Operadores maximales ; Espacios LP ; Integrales singulares
Código MathReviews MR1617657
Código Z-Math Zbl 0893.42011
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