# Parabolic equations involving Bessel operators and singular integrals

## TL;DR

This paper studies Bessel parabolic equations involving singular integrals, establishing weighted Sobolev inequalities for solutions to these equations, which are relevant for understanding their regularity and behavior.

## Contribution

It introduces new weighted Sobolev inequalities for Bessel parabolic equations using singular integral techniques, advancing the analysis of such equations.

## Key findings

- Established weighted Sobolev inequalities for Bessel parabolic equations
- Applied singular integral methods in a parabolic context
- Provided tools for analyzing regularity of solutions

## 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.