AN UPBOUND OF HAUSDORFF’S DIMENSION OF THE DIVERGENCE SET OF THE FRACTIONAL SCHRODINGER OPERATOR ON H^(s)(R^(n))

摘要

Given n≥2 and α≥1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schrodinger operator;that is,supf∈H^(s)(R^(n)) dim_(H){x∈R^(n):limt→0 e^(it)(-△)^(α) f(x)≠f(x)}≤n+1-2(n+1)s/n for n/2(n+1)