Right inverses for partial differential operators on Fourier hyperfunctions
Volume 183 / 2007
Studia Mathematica 183 (2007), 273-299
MSC: Primary 35E20; Secondary 46A63, 46F15.
DOI: 10.4064/sm183-3-5
Abstract
We characterize the partial differential operators $P(D)$ admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual $( \overline{\Omega})$-type estimate valid for the bounded holomorphic functions on the characteristic variety $V_P$ near $\mathbb R^d$. The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén–Lindelöf-type condition.
