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The A∞-Property of the Kolmogorov Measure
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Uppsala Univ, Dept Math, Uppsala, Sweden..
2017 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 10, no 7, p. 1709-1756Article in journal (Refereed) Published
Abstract [en]

We consider the Kolmogorov-Fokker-Planck operator K := Sigma(m)(i=1) partial derivative(xixi) + Sigma(m)(i=1) x(i)partial derivative(yi) - partial derivative(t) in unbounded domains of the form Omega={(x,x(m),y,y(m),t) RN+1 vertical bar x(m)>psi(x,y,t)}. Concerning and psi, we assume that Omega is what we call an (unbounded) admissible Lip(K)-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 Lip(K)-domains the associated parabolic measure is absolutely continuous with respect to a surface measure and that the associated Radon-Nikodym derivative defines an A(infinity) weight with respect to this surface measure. Our result is sharp.

Place, publisher, year, edition, pages
2017. Vol. 10, no 7, p. 1709-1756
Keywords [en]
Kolmogorov equation, ultraparabolic, hypoelliptic, Lipschitz domain, doubling measure, parabolic measure, Kolmogorov measure, A(infinity)
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-335534DOI: 10.2140/apde.2017.10.1709ISI: 000409094100005OAI: oai:DiVA.org:uu-335534DiVA, id: diva2:1163804
Funder
Göran Gustafsson Foundation for Research in Natural Sciences and MedicineAvailable from: 2017-12-08 Created: 2017-12-08 Last updated: 2017-12-08Bibliographically approved

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