复合算子与微分算子乘积的有界性和紧性.pdf

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1、EÜŽf†‡©Žf¦Èk.5Ú;5TheboundednessandcompactnessoftheproductsofdierentiationandcompositionoperatorsƉ;’µA^êÆïÄ)µL•“µ±LuÇU9ŒÆnÆ"˜c8ÕM5(²<(²¤¥ÆØ©´<3“•e?1ïÄóŠÚïĤJ§Ø©¥AO±I5Ú—ƒ?§Ø©¥Ø•¹Ù¦<®²uL½>LïĤJ§•Ø•¹•¼U9ŒÆ½Ù¦˜ÅƽyÖ¦^Lá.†·˜Ó

2、óŠÓ“éïĤ‰?Ûzþ®3Ø©¥Š²(`²¿L«¿.ÆØ©Šö¶µiFÏ:cFÆØ©‡¦^ÇÖÆØ©Šö)U9ŒÆk'3!¦^ÆØ©5½.AÇU9ŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢§¿æ^K

3、Ä1N´¼ê˜m§¤±ù~„Žf7´d,¼êѧl·‚I‡&?ùŽf5Ÿ†§‚p¼êkNS3éX©©Ì‡ïÄü¥þdk.)Û˜mBloch˜m9Zygmund˜mEÜŽf†‡©Žf¦ÈC'R,RC'5Ÿ§‰ÑC'RŽfk.5Ú;5d^‡9RC'Žfk.5Ú;5¿©^‡Ú7‡^‡©©
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4、•‡óä§3e©¥òØ2y²†A^©1nÙ´é˜a¦ÈŽf5Ÿïħ̇^®•ÚnÚ(؉ÑdaŽfk.5Ú;5d^‡§¿±½n/ª‰ÑäNy²©1oÙ†1nÙaq§´é,˜a¦ÈŽfïħ̇^®•ÚnÚ(؉ÑdaŽfk.5Ú;5¿©^‡Ú7‡^‡§¿±½n/ª‰ÑäNy².1ÊÙ´éŸØ©o(§¿Jјÿ™)û¯KÚ?˜ÚïÄ••©'…cµEÜŽf¶‡©Žf¶k.5¶;5AbstractOperatortheoryinfunctionspacesbec

5、omesahotissueofresearch.Asthecarrierofresearchisfunctionspaces,thecommonoperatormustbederivedfromcertainfunction,soweneedtodiscusstherelationbetweentheoperatorandthefunction.Inthispaper,wecharacterizetheproductsofthedierentiationandcompositionoperat

6、orsactingfromtheboundedfunctionspacetotheBlochspaceorZygmundspaceintheball,andnecessaryandsucientconditionsaregivenforthedierencetobeboundedandcompact.Thepaperismainlydividedintovechapters.Therstchapteristheintroductionofthewholepaper.Wetalkabou

7、ttheback-groundofthispaper,andmakeplansfortheresearchoftheproblem.Nextchapterofthepaper,someimportantconceptsandlemmaswhicharerelatedtothearticlearegiven.Theyarethefoundationsandtoolsofthelaterwork,andwewillusethemwithoutproof.Thethirdchapterdiscusse

8、sthepropertiesoftheproductoperators,usingthelemmaandconclusions,theequivalentconditionsofboundednessandcompactnessofoperatorsaregiven.Thefourthchapter,similarwiththethird,discussanothertypeofproductopera-tors.Atlast,wesummarizetheworkofthewholepapera