Heisenberg群上的（p，Φ）-容量.pdf

1、浙江大學理學院碩士學位論文Heisenberg群上的（p，Φ）容量姓名：周婕申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：王偉20070501AbstractInchapter2wegeneralizethedefinitionofcapaci哆onEuclidspacetotheHeisenbergLetQbeadomainintheHeisenberggroup，letFbeacompactsubsetinQandlet圣($，f)be

2、acontinuousfunctiononnⅡ耍nwhichisnonnegativeandpositivehomogeneousofthefirstdegreewithrespectto∈inf上降(毛VH讓)】‰，u∈9t(F’Q))，iscalledthe0，垂)capacityofFrelativetoQanddenotedby∞，圣)cap(FQ)Here吼(FQ)=扣∈cT(Q)：釷≥lonF)Andthenwegetthe

3、formulafoft倫pcapacityasanintegraloverlevelsurfacesaccordingtheCoareaformulaOntheStratifiedgroup：、r，‘dr111p_cap限喲。刪in刪f上萬而若蕊硒rwhereQisadomainintheHeisenberggroupandFisanycompactsubsettofLP≥1Q=2n2Thenwegetthelowerestimates

4、forthepcapacitybyusingtheisoperimetricinequalityOnHeisenberggroup：Pcap(Fn)PQ泵薪甲’～when刪p#QforSOmeconstantC≥0Inchapter3wemakesomeestimatesforthepcapacityespeciallyoftheestimatefortheintegralcontainingthepcapacityofthesetNt

5、WealsoobtaintheSobolevtypeinequalityinOrliczI101TlIOiltheHeisenberggroupandtheconditionsforthevalidityofthemultiplicativeSobolevtypeinequalityKeyWords：HeisenberggroupcapacityHorizontalgradientCoareaformulaisoperimetricin