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.