Abstract:We study singular integral operators with variable Calderón--Zygmund kernels and their commutators with $VMO$ functions in the framework of Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in $L^\Phi$ under standard $\Delta_2$ and $\nabla_2$ conditions on the Young function. The proofs rely on decomposition techniques and weak-type estimates. As an application, these results provide a functional-analytic foundation for a priori estimates and interior regularity of solutions to higher-order elliptic operators with discontinuous coefficients.
| Comments: | 15 pages |
| Subjects: | Analysis of PDEs (math.AP) |
| MSC classes: | 30H35, 32A37, 35D35, 35J48, 35J58, 42B20, 42B25, 46E30, 46E35, 47G10 |
| Cite as: | arXiv:2605.25780 [math.AP] |
| (or arXiv:2605.25780v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25780 arXiv-issued DOI via DataCite (pending registration) |
From: Lyoubomira Softova Palagacheva [view email]
[v1]
Mon, 25 May 2026 12:28:11 UTC (20 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。