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Turkish Journal of Mathematics

Authors

ÇAĞLA SEKİN

DOI

10.3906/mat-2008-26

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.

First Page

566

Last Page

578

Included in

Mathematics Commons

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