Estimates for singular integrals on homogeneous groups
Shuichi Sato

TL;DR
This paper establishes new $L^p$ boundedness and weighted inequalities for singular integral operators with rough kernels on homogeneous groups, using extrapolation techniques under sharp kernel conditions.
Contribution
It provides novel $L^p$ estimates and weighted inequalities for singular integrals on homogeneous groups, extending classical results to rough kernels.
Findings
Proved $L^p$ boundedness of singular integrals with rough kernels.
Established weighted $L^p$ inequalities for these operators.
Derived sharp conditions for kernel estimates.
Abstract
We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply boundedness of them by an extrapolation argument under a sharp condition for the kernels. Also, we prove some weighted inequalities for the operators.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Advanced Mathematical Physics Problems
