Convolution with measures on flat curves in low dimensions
Daniel M. Oberlin
TL;DR
This paper establishes convolution estimates for affine arclength measures on specific flat curves in low-dimensional spaces, advancing understanding in harmonic analysis.
Contribution
It provides new convolution estimates for affine arclength measures on flat curves in dimensions 2 to 4, a previously less understood area.
Findings
Convolution estimates are proved for flat curves in 2D, 3D, and 4D.
Results extend harmonic analysis techniques to flat curves.
New bounds for affine arclength measures are established.
Abstract
We prove convolution estimates for affine arclength measure on certain flat curves in dimensions 2, 3, and 4.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Geometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering