Bi-Parametric Potentials, Relevant Function Spaces and Wavelet-Like Transforms
INTEGRAL EQUATIONS AND OPERATOR THEORY, vol.65, no.2, pp.151-167, 2009 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 65 Issue: 2
- Publication Date: 2009
- Doi Number: 10.1007/s00020-009-1707-9
- Journal Name: INTEGRAL EQUATIONS AND OPERATOR THEORY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.151-167
- Keywords: Fractional integral, Bessel potential, semigroup, wavelet transforms, Sobolev-type space, BESSEL POTENTIALS, INVERSION, INTEGRALS
- Akdeniz University Affiliated: Yes
Abstract
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).