Bi-Parametric Potentials, Relevant Function Spaces and Wavelet-Like Transforms

ALİYEV İ.

INTEGRAL EQUATIONS AND OPERATOR THEORY, cilt.65, sa.2, ss.151-167, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s00020-009-1707-9
  • Dergi Adı: INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.151-167
  • Anahtar Kelimeler: Fractional integral, Bessel potential, semigroup, wavelet transforms, Sobolev-type space, BESSEL POTENTIALS, INVERSION, INTEGRALS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We introduce new potential type operators J(beta)(alpha) = (E+(-Delta)(beta/2))(-alpha/beta) (alpha > 0, beta > 0), and bi-parametric scale of function spaces H(beta,p)(alpha)(R(n)) associated with J(beta)(alpha). These potentials generalize the classical Bessel potentials (for beta = 2), and Flett potentials (for beta = 1). A characterization of the spaces H(beta,p)(alpha)(R(n)) is given with the aid of a special wavelet-like transform associated with a beta-semigroup, which generalizes the well-known Gauss-Weierstrass semigroup (for beta = 2) and the Poisson one (for beta = 1).