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Parabolic weighted norm
inequalities and partial differential equations
Juha Kinnunen and Olli Saari |
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Vol. 9 (2016), No. 7, 1711–1736
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DOI: 10.2140/apde.2016.9.1711
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Abstract |
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We introduce a class of weights related to the regularity theory of nonlinear parabolic partial differential equations. In particular, we investigate connections of the parabolic Muckenhoupt weights to the parabolic BMO. The parabolic Muckenhoupt weights need not be doubling and they may grow arbitrarily fast in the time variable. Our main result characterizes them through weak- and strong-type weighted norm inequalities for forward-in-time maximal operators. In addition, we prove a Jones-type factorization result for the parabolic Muckenhoupt weights and a Coifman–Rochberg-type characterization of the parabolic BMO through maximal functions. Connections and applications to the doubly nonlinear parabolic PDE are also discussed. |
Keywords
parabolic BMO, weighted norm inequalities, parabolic PDE,
doubly nonlinear equations, one-sided weight
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Mathematical Subject Classification 2010
Primary: 42B25, 42B37, 35K55
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Milestones
Received: 15 February 2016
Revised: 20 June 2016
Accepted: 28 August 2016
Published: 7 November 2016
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Authors |
| Juha Kinnunen | |
| Department of Mathematics %, School of Science Aalto University P.O. Box 11100 FI-00076 Aalto Finland |
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| Olli Saari | |
| Department of Mathematics Aalto University P.O. Box 11100 FI-00076 Aalto Finland |
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