文档介绍：AnalysisinTheoryandApplications
Volume24Number42008,336350
DOIJ007I049600803365
GENERALIZEDBESOVSPACES
ANDTRIEBELLIZORKINSPACES
HuikunJiang
NaningUniversinChinal
ChinChengin
enionalConpalUniversinyChinafTaiwan
RecevedJune16,2008
AbstractIispaperthecltssiealBesoyspaces邢andTebeLizotkinspaeesF
generalizedBesoyspaeesandThicbeLLizorkinspaeesdenoedy能yandFRyfor&e酮
and人EMrspectivelykeepmanyinterestingproperiessuchssembeddingtheoreng
Cwilsealesproperyforallsnootnessweight,ifingproperiesforllpammeler政
andduatiyforindex0一一心Byconsractnganexampleifishownlhattherea
infnitelymanygeneradizedBesoyspacesandgeneriizedTeheLizorkinspacesVing
between邹nandU劲andbebween应yandUtorespeetively
RKeywordsBesovpaceenbeddingheoromfincfionspaceofgeneralzedmooineay
ThiebelLicorkinpace
AMSQ000sobjectclassifeationt42C99
1Introduction
thispapertheBesovspaces印andTriebeLizorkinspacesPygforse叉aregeneralized
inanisotopywaywiththesmoothnessweights{佩宏oTheseclssicalspaces动and
containmanywelLknownfunctionspacesasspecialcasesstchastheLipsehitzspacesAjgR
introducedbyBesovl,theZygmundspacesrRinuoducedbyZygmundiltheSlopodeckij
,andthe
BesepotentialspacesHRintoducedbyAronszajn,SmithtlandCalderdnblandsoon
Furthermoretheyhavethescalespropertyliat股,R0C动,R0and邦RJC武
s1ee08,p4
SipoHNSFCTCHiuRrGnntlo5I08tamdbyNSCinTiipsionderGnntNSC92115W008009
ffortiesecondauton
Analysis加TheoryandApplicationsWoL24No42008337
Theftnctionspaces彤qand应havebeengeneralizedbyseveralauthorswithdifferent
spacesintheisotropieway,In6lMourausedthesequence{20Y2刀}7owithanadmisible
generalizedtheftnctionspacesaboveinan
functionyinsteadofthesmoothnessweight277oandgeneralized股t招
,FarkasandLeopoldsedmoregeneralsmoothnessweightanadmissiblese
quenceajzoinsteadof20oaswellasusedthesequenceNJoinseadof21仪