On behaviour of the Riesz and generalized Riesz potentials as order tends to zero

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Gadjiev A. D., Aral A., ALİYEV İ.

MATHEMATICAL INEQUALITIES & APPLICATIONS, vol.10, no.4, pp.875-888, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.7153/mia-10-80
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.875-888
  • Keywords: Riesz potentials, generalized translation operator, d-point, Lipschitz point, approximation, modulus of continuity
  • Akdeniz University Affiliated: Yes


In this paper, we present the Riesz potentials I-alpha and the generalized Riesz potentials I-v(alpha) as the families of positive linear operators, depending on parameter alpha > 0. We investigate their pointwise convergence and convergence in the norm as alpha -> 0. We investigate also the order of approximation of these families and show in particular that the order of approximation at the Lipschitz points is independent from Lipschitz degree.