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The  $A_\infty$-property of the Kolmogorov measure
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206XArticle in journal (Refereed) Accepted
Abstract [en]

We consider the Kolmogorov-Fokker-Planck operator              \begin{eqnarray*}\label{e-kolm-nd}   \K:=\sum_{i=1}^{m}\partial_{x_i x_i}+\sum_{i=1}^m x_i\partial_{y_{i}}-\partial_t,    \end{eqnarray*}    in unbounded domains of the form         \begin{eqnarray*}\label{dom} \Omega=\{(x,x_{m},y,y_{m},t)\in\mathbb R^{N+1}:\ x_m>\psi(x,y,t)\}.    \end{eqnarray*}    Concerning $\psi$ and $\Omega$ we assume that $\Omega$ is what we call an (unbounded) admissible $\MLip$-domain: $\psi$ satisfies a    uniform Lipschitz condition, adapted to the dilation structure and the (non-Euclidean) Lie group underlying    the operator $\K$, as well as an additional regularity condition formulated in terms of a Carleson measure. We prove that in   admissible $\MLip$-domains the associated parabolic measure is absolutely continuous with respect to a surface measure and that    the associated Radon-Nikodym derivative defines an $A_\infty$ weight with respect to this surface measure. Our result is sharp.

Place, publisher, year, edition, pages
2016.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-280644OAI: oai:DiVA.org:uu-280644DiVA: diva2:911517
Available from: 2016-03-13 Created: 2016-03-13 Last updated: 2017-06-25

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Nyström, Kaj

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