Rough maximal functions and rough singular integral operators applied to integrable radial functions.

Sjögren, Peter, and Soria, Fernando. "Rough maximal functions and rough singular integral operators applied to integrable radial functions.." Revista Matemática Iberoamericana 13.1 (1997): 1-18. <http://eudml.org/doc/39531>.

@article{Sjögren1997,
abstract = {Let Ω be homogeneous of degree 0 in Rn and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor Ω in the definition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels Ω(y) / |y|n, provided that the mean value of Ω vanishes. In an earlier paper, the authors showed that a two-dimensional rough maximal operator is of weak type (1,1) when restricted to radial functions. This result is now extended to arbitrary finite dimension, and to rough singular integrals.},
author = {Sjögren, Peter, Soria, Fernando},
journal = {Revista Matemática Iberoamericana},
keywords = {Integrales singulares; Teoría de la aproximación; Operadores maximales; Operadores integrales; Dimensiones; Función distribución radial; Integrabilidad; Finitud; maximal operator; singular integral operator; weak type (1,1)},
language = {eng},
number = {1},
pages = {1-18},
title = {Rough maximal functions and rough singular integral operators applied to integrable radial functions.},
url = {http://eudml.org/doc/39531},
volume = {13},
year = {1997},
}

TY - JOUR
AU - Sjögren, Peter
AU - Soria, Fernando
TI - Rough maximal functions and rough singular integral operators applied to integrable radial functions.
JO - Revista Matemática Iberoamericana
PY - 1997
VL - 13
IS - 1
SP - 1
EP - 18
AB - Let Ω be homogeneous of degree 0 in Rn and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor Ω in the definition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels Ω(y) / |y|n, provided that the mean value of Ω vanishes. In an earlier paper, the authors showed that a two-dimensional rough maximal operator is of weak type (1,1) when restricted to radial functions. This result is now extended to arbitrary finite dimension, and to rough singular integrals.
LA - eng
KW - Integrales singulares; Teoría de la aproximación; Operadores maximales; Operadores integrales; Dimensiones; Función distribución radial; Integrabilidad; Finitud; maximal operator; singular integral operator; weak type (1,1)
UR - http://eudml.org/doc/39531
ER -