Document Type
Honors Project - Open Access
Abstract
The Brascamp-Lieb inequality is a generalization of many well-known multilinear functional inequalities. The Brascamp-Lieb constant is the best constant that works for the Brascamp-Lieb inequality for a given tuple of input linear maps and powers. If we keep the powers constant while varying the input linear maps, the Brascamp-Lieb constant becomes a function of the linear maps. In this thesis, we explore the Hölder continuity of the Brascamp-Lieb constant. Specifically,we prove that the general 4-linear case of the Brascamp-Lieb inequality is locally Lipschitz continuous. Additionally, we provide an improvement of a previous result on the local Hölder continuity of the Brascamp-Lieb constant.
Recommended Citation
Friesen, Ori, "On the Hölder Continuity of the Brascamp-Lieb Constant" (2025). Mathematics, Statistics, and Computer Science Honors Projects. 98.
https://digitalcommons.macalester.edu/mathcs_honors/98
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