Parabolic weighted norm inequalities and partial differential equations

Abstract

We investigate parabolic Muckenhoupt weights and functions of bounded mean oscillation (BMO) related to nonlinear parabolic partial differential equations. The main result gives a full characterization of weak and strong type weighted norm inequalities for parabolic forward in time maximal operators. In addition, we give a Jones type factorization result for the parabolic Muckenhoupt weights and a Coifman-Rochberg type characterization of the parabolic BMO from Moser's seminal paper through parabolic Muckenhoupt weights and maximal functions.

29 pages. To appear in Anal. PDE. Referee's corrections incorporated. Small change in the title

References in corpus (1)

• Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations

Cited by in corpus (2)

• Parabolic BMO and the forward-in-time maximal operator
• Parabolic Muckenhoupt Weights Characterized by Parabolic Fractional Maximal and Integral Operators with Time Lag