1、青島大學(xué)碩士學(xué)位論文兩類奇異積分算子交換子的某些有界性姓名：葛蕾申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：趙凱20071202AbstractInthisthesis，wediscusstheboundedne88oftwotypesofcommutatorsonweightedHerztypespaces，whichare【b，卅generatedbygeneralizedCalder6nZygmundoperatorsTwithLi

2、pschitzfunctionbandaclassofMarcinkiewiczintegralcommutatorsp‘l，bgeneratedbyBMO(R”)functionsandMarcinkiewiczintegralswithroughkernelsThisthesisconsistsofthefollowingpartsInthefirstchapter，usingthedecompositionofHerztypeHa

3、rdyspacesintermsofcentralatomsandthepropertiesofA1，theboundednessoftheeom—mutatorfb，卅generatedbygeneralizedCalder6nZygmundoperatorsTwithLipschitzfunctionbisstudiedWeshowthat【b，卅isboundedfromhomogeneousHerztypeHardyspaceH

4、Kqalm(ul，迸1)tohomogeneousHerzspace垤船(‰謬)Andwealsoobtainthat[6，卅isboundedfromhomogeneousHerztypeHardyspacetohomogeneousHerzspaceoncriticalpoints。ForthenonhomogeneousHerzspaces，wehavethesimilarresultsInthesecondchapter，the

5、boundednessonhomogeneousweightedHerzspacesisestablishedforaclassofMarcinkiewiczintegralcommutatorsp‘1bgeneratedbyBMO(R1)functionsandMarcinkiewiezintegralswithroughkernelsThemainresultsarededucedfromthedefinitionsofK囂p2(u

6、1，u字)BytheMinkowskiintegralinequalityandtheJenseninequalitytocontrolsomeinequalities，weobtaintheboundednessofMarcinkiewiczintegralcommutatorspn，bonweightedHerzspaceswhenQ，口satisfytwokindsofdifferentconditionsKeywords：Her