Scaling invariant Harnack inequalities in a general setting

Hansen W, Netuka I (2016)
Journal of Mathematical Analysis and Applications 444(2): 980-999.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Hansen, WolfhardUniBi; Netuka, Ivan
Abstract / Bemerkung
In a setting, where only "exit measures" are given, as they are associated with an arbitrary right continuous strong Markov process on a separable metric space, we provide simple criteria for the validity of Harnack inequalities for positive harmonic functions. These inequalities are scaling invariant with respect to a metric on the state space which, having an associated Green function, may be adapted to the special situation. In many cases, this also implies continuity of harmonic functions and Holder continuity of bounded harmonic functions. The results apply to large classes of Levy (and similar) processes. (C) 2016 Elsevier Inc. All rights reserved.
Stichworte
Harnack inequality; Holder continuity; Levy process; Green function; Krylov-Safonov estimate; Ikeda-Watanabe formula
Erscheinungsjahr
2016
Zeitschriftentitel
Journal of Mathematical Analysis and Applications
Band
444
Ausgabe
2
Seite(n)
980-999
ISSN
0022-247X
eISSN
1096-0813
Page URI
https://pub.uni-bielefeld.de/record/2905953

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Hansen W, Netuka I. Scaling invariant Harnack inequalities in a general setting. Journal of Mathematical Analysis and Applications. 2016;444(2):980-999.
Hansen, W., & Netuka, I. (2016). Scaling invariant Harnack inequalities in a general setting. Journal of Mathematical Analysis and Applications, 444(2), 980-999. doi:10.1016/j.jmaa.2016.06.069
Hansen, W., and Netuka, I. (2016). Scaling invariant Harnack inequalities in a general setting. Journal of Mathematical Analysis and Applications 444, 980-999.
Hansen, W., & Netuka, I., 2016. Scaling invariant Harnack inequalities in a general setting. Journal of Mathematical Analysis and Applications, 444(2), p 980-999.
W. Hansen and I. Netuka, “Scaling invariant Harnack inequalities in a general setting”, Journal of Mathematical Analysis and Applications, vol. 444, 2016, pp. 980-999.
Hansen, W., Netuka, I.: Scaling invariant Harnack inequalities in a general setting. Journal of Mathematical Analysis and Applications. 444, 980-999 (2016).
Hansen, Wolfhard, and Netuka, Ivan. “Scaling invariant Harnack inequalities in a general setting”. Journal of Mathematical Analysis and Applications 444.2 (2016): 980-999.