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/...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)<s≤n/2.展开更多
We investigate the refined Carleson’s problem of the free Ostrovsky equation{ut+■_(z)^(3)u+■_(x)^(-1)u=0,u(x,0)=f(x)where(x,t)∈R×R and f∈H^(s)(R).We illustrate the Hausdorff dimension of the divergence set f...We investigate the refined Carleson’s problem of the free Ostrovsky equation{ut+■_(z)^(3)u+■_(x)^(-1)u=0,u(x,0)=f(x)where(x,t)∈R×R and f∈H^(s)(R).We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equationα1,U(s)=1-2 s,1/4≤s≤1/2.展开更多
基金Li Dan and Li Junfeng were supported by NSFC-DFG(11761131002)NSFC(12071052)Xiao Jie was supported by NSERC of Canada(202979463102000).
文摘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)<s≤n/2.
基金supported by the National Natural Science Foundation of China(11571118,11401180 and 11971356)。
文摘We investigate the refined Carleson’s problem of the free Ostrovsky equation{ut+■_(z)^(3)u+■_(x)^(-1)u=0,u(x,0)=f(x)where(x,t)∈R×R and f∈H^(s)(R).We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equationα1,U(s)=1-2 s,1/4≤s≤1/2.
