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<p>We prove regularity results in weighted Sobolev and Besov spaces, both for the stationary and evolution equations driven by a class of differential and pseudo-differential operators. These properties are related to the smoothing properties of the associated generalised Mehler semigroups generated by nonlocal operators of the form (<InternalRef RefID="Equ7">1.7</InternalRef>). In particular, our regularity results can be applied to Ornstein-Uhlenbeck operators with fractional diffusion.</p>

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Regularity results for generalised Mehler semigroups in \(L^p\) spaces with respect to invariant measures

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Luciana Angiuli,
  • Simone Ferrari,
  • Diego Pallara

摘要

We prove regularity results in weighted Sobolev and Besov spaces, both for the stationary and evolution equations driven by a class of differential and pseudo-differential operators. These properties are related to the smoothing properties of the associated generalised Mehler semigroups generated by nonlocal operators of the form (1.7). In particular, our regularity results can be applied to Ornstein-Uhlenbeck operators with fractional diffusion.