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

Revista Matemática Iberoamericana (1997)

- Volume: 13, Issue: 1, page 1-18
- ISSN: 0213-2230

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topSjögren, 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 -

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