2020/05/31 by Behnam Esmayli, Piotr Hajłasz, Esmayli, Behnam +1 · 1 citation
Mathematics · #28A25 #28A75 #28A78 #30L #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:28A25 #msc:28A75 #msc:28A78 #msc:30L
paper · pdf · doi:10.48550/arxiv.2006.00419
arxiv created 2020/06/11 · arxiv updated 2020/06/12
The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all details. The known proof is based on a difficult result of Davies. Our proof is elementary and does not use Davies' theorem. Instead we use an elegant argument that we learned from Nazarov through MathOverflow. We also obtain some generalizations of the coarea inequality.