Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients
Functional Analysis
2023-02-24 v2 Analysis of PDEs
Classical Analysis and ODEs
Abstract
We prove a bi-sublinear embedding for semigroups generated by non-smooth complex-coefficient elliptic operators in divergence form and for certain mutually dual pairs of Orlicz-space norms. This generalizes a result by Carbonaro and Dragi\v{c}evi\'{c} from power functions to more general Young functions that still behave like powers. To achieve this, we generalize a Bellman function constructed by Nazarov and Treil.
Cite
@article{arxiv.2110.15812,
title = {Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients},
author = {Vjekoslav Kovač and Kristina Ana Škreb},
journal= {arXiv preprint arXiv:2110.15812},
year = {2023}
}
Comments
23 pages; v2: referee's suggestions incorporated, accepted for publication