; TeX output 2005.04.04:0851 c hGS 9K`y UU cmr10AnnalesAcademiScienĽtiarumFN8ennic MathematicaVN8olumen30,2005,99{111čZYw7"V cmbx10Ha Dj *lasz{Sobb"olevtypespacesand~YYTLb> cmmi10Lp -energyontheSierpinskigasket^n"V cmbx10JiaxinTHu,Y uanJi,andZhiyingWenRTsinghĽuaUniversityN8,DepartmentofMathematicalSciences ?HBeijing100084,China nJXHu@math.tsinghĽua.edu.cn;jiyuan00@mails.tsinghua.edu.cn;wenzy@tsinghua.edu.cnD"V UU cmbx10DAbstract.WN8e/mstudyHavj glasz{Sob;BolevtĽypespacesonmetricspacesthatdependonquasi- distances;inparticular,+wĽemaytakethequasi-distancetob;BethepoĽwer<b> UU cmmi10ofthemetricwith>P1 ,ifnthemetricspaceishighlyirregularorp;Borous.WN8etakĽetheSierpinskigasketinnDR:ٓR U cmr72[asanexample,andshoĽwthattheHavj glasz{Sob;Bolevtyp;Bespaceisnon-trivialfor1<I<?=0er U cmmi7po=pwith?pcĽharacterizing?theintrinsicprop;BertyoftheSierpinskigasket.dThisworkwasstronglymotiv{atedbĽy[8],andgeneralizestheresultin[9]toany1P