An Extension of Hörmander’s Hypoellipticity Theorem

David P. Herzog, Nathan Totz

Research output: Contribution to journalArticlepeer-review


Motivated by applications to stochastic differential equations, an extension of Hörmander’s hypoellipticity theorem is proved for second-order degenerate elliptic operators with non-smooth coefficients. The main results are established using point-wise Bessel kernel estimates and a weighted Sobolev inequality of Stein and Weiss. Of particular interest is that our results apply to operators with quite general first-order terms.

Original languageEnglish (US)
Pages (from-to)403-433
Number of pages31
JournalPotential Analysis
Issue number2
StatePublished - Feb 2014
Externally publishedYes


  • Degenerate stochastic differential equations
  • Hypoellipticity
  • Hörmander’s theorem
  • Malliavin calculus
  • Pseudo-differential calculus

ASJC Scopus subject areas

  • Analysis


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