Andforanyα>0,theLaplaciansatisfies Gλ c1 2α Gλ+2Md whereM =c23α/c1+c22. 2. IfG (x)=kg (x)k2 isC1,then k G (x)k c2kg (x)k,g (x) > G (x) c1G (x). Proof. Claim1.Note Gλ =2 2Fλgλandthat 1 2 c1I 2Fλ= mX