Parabolic equations involving Bessel operators and singular integrals

Abstract

In this paper we consider the evolution equation ${\partial }_{t}u={\Delta }_{\mu }u+f$ and the corresponding Cauchy problem, where ${\Delta }_{\mu }$ represents the Bessel operator ${\partial }_x^2+(\frac{1}{4}-{\mu }^2)x^{-2}$, for every $\mu >-1$. We establish weighted and mixed weighted Sobolev type inequalities for solutions of Bessel parabolic equations. We use singular integrals techniques in a parabolic setting.

References in corpus (1)

• On weighted mixed-norm Sobolev estimates for some basic parabolic equations