Parabolic Equations Involving Bessel Operators and Singular Integrals

  • J. J. Betancor
  • M. De León-Contreras


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.


Parabolic equations Riesz transforms Weighted inequalities Bessel operators 

Mathematics Subject Classification

Primary 42B25 42B15 Secondary 42B20 46B20 46E40 



The authors thank Professor José Luis Torrea (UAM, Madrid) for posing the problems studied in this paper and for reading a first version of the manuscript. His comments have allowed us to improve Theorem 1.5 and its proof.


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Authors and Affiliations

  1. 1.Departamento de Análisis MatemáticoUniversidad de La LagunaSan Cristóbal de La LagunaSpain
  2. 2.Departamento de Matemáticas Facultad de CienciasUniversidad Autónoma de MadridMadridSpain

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