The Kato square root problem for parabolic operators with an anti-symmetric part in BMO

TL;DR

This paper addresses the Kato square root problem for a class of parabolic operators with complex coercive parts and anti-symmetric BMO coefficients, including some unbounded cases.

Contribution

It extends the Kato square root problem solution to parabolic operators with anti-symmetric BMO coefficients, allowing for unbounded coefficients.

Findings

Established the Kato square root estimate for the specified class of operators.

Included operators with unbounded coefficients in the analysis.

Provided new techniques for handling anti-symmetric BMO parts.

Abstract

We solve the Kato square root problem for parabolic operators whose coefficients can be written as the sum of a complex part, which is coercive, and a real anti-symmetric part, which is in BMO. In particular, we allow for certain unbounded coefficients.