Abstract.
We introduce new potential type operators \(J^{\alpha}_{\beta} = (E+(-\Delta)^{\beta/2})^{-\alpha/\beta}\), (α > 0, β > 0), and bi-parametric scale of function spaces \(H^{\alpha}_{\beta , p}({\mathbb{R}}^n)\) associated with Jαβ. These potentials generalize the classical Bessel potentials (for β = 2), and Flett potentials (for β = 1). A characterization of the spaces \(H^{\alpha}_{\beta, p}({\mathbb{R}}^n)\) is given with the aid of a special wavelet–like transform associated with a β-semigroup, which generalizes the well-known Gauss-Weierstrass semigroup (for β = 2) and the Poisson one (for β = 1).
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
The author was supported by the Scientific Research Project Administration Unit of the Akdeniz University and TUBITAK.
Rights and permissions
About this article
Cite this article
Aliev, I.A. Bi-Parametric Potentials, Relevant Function Spaces and Wavelet-Like Transforms. Integr. equ. oper. theory 65, 151 (2009). https://doi.org/10.1007/s00020-009-1707-9
Received:
Revised:
Published:
DOI: https://doi.org/10.1007/s00020-009-1707-9