Fractional differentiation for the Gaussian measure and applications
The authors define the fractional derivative of order \(\alpha\) such that \(0<\alpha< 1\), associated with respect to Gaussian measure. Characterization of the Gaussian potential spaces is obtained in terms of the fractional derivative operators, defined in this paper, to study the relation between potential spaces \(L^p_k(\gamma_1)\) and Sobolev spaces \(W^p_k(\gamma_1)\). Indeed, the authors have extensively written the section of introduction by presenting all possible terminologies and various definitions. The analyses, employed in proving the theorems, are explicit and comprehensive. The paper concludes by obtaining Calderon's reproduction formula for the Gaussian measure in terms of this fractional derivative.
scientific article; zbMATH DE number 2132860