Variation and oscillation for harmonic operators in the inverse Gaussian setting

Abstract

<p style='text-indent:20px;'>We prove variation and oscillation <inline-formula><tex-math id="M1">\begin{document}$ L^p $\end{document}</tex-math></inline-formula>-inequalities associated with fractional derivatives of certain semigroups of operators and with the family of truncations of Riesz transforms in the inverse Gaussian setting. We also study these variational <inline-formula><tex-math id="M2">\begin{document}$ L^p $\end{document}</tex-math></inline-formula>-inequalities in a Banach-valued context by considering Banach spaces with the UMD-property and whose martingale cotype is fewer than the variational exponent. We establish <inline-formula><tex-math id="M3">\begin{document}$ L^p $\end{document}</tex-math></inline-formula>-boundedness properties for weighted difference involving the semigroups under consideration.</p>