复合算子的代数性质.pdf

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5、compositionoperatorsinanalyticfunctionspacesareim-portantcomponentpartsinoperatorelds.Inthispaper,wecharacterizeessentialcommutativityoftheintegraloperatorsandcompositionoperators,theboundednessandcompactnessoftheweighteddierentiationcompositionoperator,andsomeasymp-toticallyequivalentexpressi

6、onsoftheessentialnormsofdierenceofproductsoftheintegraltypeandcompositionoperatorsinsomeanalyticfunctionspaces.Thepaperismainlydividedintovechapters.Therstchapteristheintroductionofthewholepaper.Wetalkabouttheback-groundofthispaper,andmakeplansfortheresearchoftheproblem.Nextchapterofthepaper,

7、someimportantconceptsandlemmaswhicharerelatedtothearticlearegiven.Theyarethefoundationsandtoolsofthelaterwork,andwewillusethemwithoutproof.Thethirdchapterdiscussesthepropertiesofessentialcommutativityoftheintegraloperatorsandcompositionoperatorsfromthemixed-normspacetotheBspaceintheunitdisk.Thef

8、ourthchaptercharacterizestheboundednessandcompactnessoftheweighteddierentiationcompositionoperatorfromweightedBergmanspaceton-thweightedspaceontheunitdiskofC.Atlast,wecharacterizestheboundednessofthedierencesoftheproductso