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

Creative Commons License

Gadjiev A. D., Aral A., ALİYEV İ.

MATHEMATICAL INEQUALITIES & APPLICATIONS, cilt.10, sa.4, ss.875-888, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 4
  • Basım Tarihi: 2007
  • Doi Numarası: 10.7153/mia-10-80
  • Dergi Adı: MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.875-888
  • Anahtar Kelimeler: Riesz potentials, generalized translation operator, d-point, Lipschitz point, approximation, modulus of continuity
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.