2013/01/09 by Stephen Lewis, Lewis, Stephen
Mathematics · #28A75 #28E99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:28A75 #msc:28E99
paper · pdf · doi:10.48550/arxiv.1301.1993
43 pages, 7 figures
arxiv created 2013/01/13 · arxiv updated 2013/01/15
We consider the question of how the doubling characteristic of a measure determines the regularity of its support. The question was considered by David, Kenig, and Toro for codimension-1 under a crucial assumption of flatness, and later by Preiss, Tolsa, and Toro in higher codimension. However, their studies leave open the geometry of the support of such measures in a neighborhood about a non-flat point of the support. We here answer the question (in an almost classical sense) for codimension-1 Hölder doubling measures in \RR4.