Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 7 (2016), 1711-1736.

Parabolic weighted norm inequalities and partial differential equations

Juha Kinnunen and Olli Saari

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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.

Article information

Anal. PDE, Volume 9, Number 7 (2016), 1711-1736.

Received: 15 February 2016
Revised: 20 June 2016
Accepted: 28 August 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory 42B37: Harmonic analysis and PDE [See also 35-XX] 35K55: Nonlinear parabolic equations

parabolic BMO weighted norm inequalities parabolic PDE doubly nonlinear equations one-sided weight


Kinnunen, Juha; Saari, Olli. Parabolic weighted norm inequalities and partial differential equations. Anal. PDE 9 (2016), no. 7, 1711--1736. doi:10.2140/apde.2016.9.1711.

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