L^p mapping properties for the Cauchy–Riemann equations on Lipschitz domains admitting subelliptic estimates

ABSTRACT

We show that on bounded Lipschitz pseudoconvex domains that admit good weight functions the $\overline{\partial }$-Neumann operators $N_q,{\overline{\partial }}^{\ast }{N}_q$, and $\overline{\partial }{N}_q$ are bounded on $L^p$ spaces for some values of p greater than 2.

KEYWORDS:

• Lipschitz domains
• good weight functions
• $\overline{\partial }$-Neumann operators

AMS SUBJECT CLASSIFICATIONS:

• 32W05
• 32W10

Acknowledgements

The authors would like to thank the referee for many helpful suggestions that have significantly improved this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the second author was partially supported by the Simons Foundation [grant number 353525].