## Analysis & PDE

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

### Parabolic weighted norm inequalities and partial differential equations

#### Abstract

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

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

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

https://projecteuclid.org/euclid.apde/1510843355

Digital Object Identifier
doi:10.2140/apde.2016.9.1711

Mathematical Reviews number (MathSciNet)
MR3570236

Zentralblatt MATH identifier
1351.42023

#### Citation

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. https://projecteuclid.org/euclid.apde/1510843355

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