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.
Regularity results for generalised Mehler semigroups in $$L^p$$ spaces with respect to invariant measures
Angiuli, Luciana;Ferrari, Simone;Pallara, Diego
2026-01-01
Abstract
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.File in questo prodotto:
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