Approximation and Interpolation in Kolmogorov-type groups

2022/05/11 by Pesce, Antonello
#35D99 #35H10 #35K65 #46M35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2205.05340

Abstract

We prove a real interpolation characterization for some non Euclidean Hölder spaces, built on the Lie structure induced by a class of ultra-parabolic Kolmogorov-type operators satisfying the Hörmander condition. As a by-product we also obtain an approximation property for intrinsically regular functions on the whole space.

Related

• Fractional Sobolev spaces related to an ultraparabolic operator
• Intrinsic Taylor formula for non-homogeneous Kolmogorov-type Lie groups
• The structure of approximate groups
• Limiting interpolation spaces via extrapolation
• Besov and Paley-Wiener spaces, Moduli of continuity and Hardy-Steklov operators associated with the group "ax+b"