25575.加權(quán)besov空間中的線性平均和隨機(jī)寬度

1、加權(quán)Besov空間中的線性平均和隨機(jī)寬度Linearandstochasticwidthsofwe：“ghtedBesovraverageanstochastlcw11sotnteesovLJWe：spaces作者：王晶晶Author：曼i望西i望g!篁塑g指導(dǎo)教師：堡奎塹Supervisor：墜堡i望Qi塑專業(yè)：計(jì)算數(shù)學(xué)Major：——ComputationalMathematics——學(xué)位：琿學(xué)塑Degree：MasterofSci

2、ence授予單位：塹’江塑整盤堂Institute：圣墮gi壘望g墮Q!坐壘!旦墜i翌!曼i!YMay2014AbstractInthispaper，weinvestigatetheasymptoticdegreesoflinearaverageandstochasticwidthsofembeddingsofweightedBesovspacesintheaveragesettingandrandomizedsettingThisth

3、esisisorganizedasfollowsInthefirstchapter，thebackgroundandsignificanceoftheresearcharepresented：Wealsointroducesomebasicsymbols，conceptsanddiscretetheweightedBesovspacesbythediscretizationmethodSomepreliminaryknowledgean

4、dthemainstructureofthispaperareoutlinedintheendThefollowingchapterconsiderstheweightedBesovspacewhichisconstructedbythecommonweightfunctionua(z)=(1Izl2)暑(X∈IRd，Q0)Wefirstestimatetheasymptoticdegreesofthelinearaverageands

5、tochasticwidthsofembeddingsofweightedsequencespacesBytheembeddingtheorem，weshifttheseresultsfromtheweightedsequencespacestotheweightedBesovspacesandobtainourmaintheoremofthecompactembeddingsId：露k(iRd口)時(shí)娣‰(IRd)(1sPl，p2，ql

6、，92≤∞，一∞82s1OO)ThethirdchapterinvestigatestheasymptoticdegreesofthelinearaverageandstochasticwidthsofthefollowingembeddingsId：娣‰(IRau)卜娣k(IRd)intheweightedBesovspacewhichisconstructedbythegeneralweightfunctionu∈W1nw2Andt