简介:Inthispaper,weconsiderthealmosteverywhereconvergencofBochner-RieszmeansbelowthecriticalindexinBesselpotentialspacesanda>0)andfindouttherelationbetweentheindexofBochner-Rieszmeansandthedegreeofsmoothnessoffunctions.
简介:Recently,Cristofaro-GardinerandHutchingsprovedthatthereexistatleasttwoclosedcharacteristicsoneverycompactstar-shapedhypersufaceinR~4.ThenGinzburg,Hein,Hryniewicz,andMacarinigavethisresultasecondproof.Inthispaper,wegiveitathirdproofbyusingindexiterationtheory,resonanceidentitiesofclosedcharacteristicsandaremarkabletheoremofGinzburgetal.