JournalsrmiVol. 13, No. 1pp. 1–18

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

  • Peter Sjögren

    Chalmers University of Technology, Göteborg, Sweden
  • Fernando Soria

    Universidad Autónoma de Madrid, Spain
Rough maximal functions and rough singular integral operators applied to integrable radial functions cover
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Abstract

Let Ω\Omega be homogeneous of degree 0 in Rn\mathbb R^n and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor Ω\Omega in the denition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels Ω(y)/yn\Omega(y)/|y|^n, provided that the mean value of Ω\Omega 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.

Cite this article

Peter Sjögren, Fernando Soria, Rough maximal functions and rough singular integral operators applied to integrable radial functions. Rev. Mat. Iberoam. 13 (1997), no. 1, pp. 1–18

DOI 10.4171/RMI/216