Parabolic BMO and the forward-in-time maximal operator

Abstract

We study if the parabolic forward-in-time maximal operator is bounded on parabolic BMO. It turns out that for non-negative functions the answer is positive, but the behaviour of sign changing functions is more delicate. The class parabolic BMO and the forward-in-time maximal operator originate from the regularity theory of nonlinear parabolic partial differential equations. In addition to that context, we also study the question in dimension one.

23 pages, 3 figures

References in corpus (2)

• Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations
• Parabolic weighted norm inequalities and partial differential equations

Cited by in corpus (1)

• Parabolic Muckenhoupt Weights Characterized by Parabolic Fractional Maximal and Integral Operators with Time Lag