Turkish Journal of Mathematics
Abstract
In this work we introduce some generalizations of the singular parabolic Riesz and parabolic Bessel potentials. Namely, $\Delta _{\nu }$ being the Laplace-Bessel singular differential operator, we define the families of operators \begin{equation*} H_{\beta ,\nu }^{\alpha }=\left( \frac{\partial }{\partial t}+(-\Delta _{\nu })^{\beta /2}\right) ^{-\alpha /\beta }\text{ and }\mathcal{H}_{\beta ,\nu }^{\alpha }=\left( I+\frac{\partial }{\partial t}+(-\Delta _{\nu })^{\beta /2}\right) ^{-\alpha /\beta }\text{ , (}\alpha ,\beta >0\text{),} \end{equation*} and investigate their properties in the special weighted $L_{p,\nu }$-spaces.
DOI
10.3906/mat-2008-26
Keywords
Laplace-Bessel differential operator, Fourier-Bessel transform, singular parabolic potentials, generalized translation operator, Hardy-Littlewood-Sobolev type inequality
First Page
566
Last Page
578
Recommended Citation
SEKİN, Ç (2021). A generalization of parabolic potentials associated to Laplace-Bessel differential operator and its behavior in the weighted Lebesque spaces. Turkish Journal of Mathematics 45 (1): 566-578. https://doi.org/10.3906/mat-2008-26
