Generalized Riesz Potential Spaces and their Characterization via Wavelet-Type Transform
FILOMAT, cilt.30, sa.10, ss.2809-2823, 2016 (SCI-Expanded)
- 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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.