Generalized Riesz Potential Spaces and their Characterization via Wavelet-Type Transform

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ALİYEV İ., Saglik E.

FILOMAT, cilt.30, sa.10, ss.2809-2823, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 10
  • Basım Tarihi: 2016
  • Doi Numarası: 10.2298/fil1610809a
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2809-2823
  • Anahtar Kelimeler: Wavelet-type transform, generalized Riesz potentials, Riesz potential spaces, semigroup, generalized translation operator
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We introduce a wavelet-type transform generated by the so-called beta-semigroup, which is a natural generalization of the Gauss-Weierstrass and Poisson semigroups associated to the Laplace-Bessel convolution. By making use of this wavelet-type transform we obtain new explicit inversion formulas for the generalized Riesz potentials and a new characterization of the generalized Riesz potential spaces. We show that the usage of the concept beta-semigroup gives rise to minimize the number of conditions on wavelet measure, no matter how big the order of the generalized Riesz potentials is.