奇异积分算子的某些问题的研究.pdf

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3、ᴀ᭛Ё៥Ӏᇚⷨおᶤѯ⿃ߚㅫᄤⱘ᳝⬠ᗻ੠ᬊᬯᗻ.ܼ᭛݅ߚЎѨゴ.㄀ϔゴҟ㒡޴㉏䞡㽕ⱘߑ᭄ぎ䯈ঞⳌ݇ㅫᄤ.㄀Ѡゴ,៥Ӏⷨおњϔ㠀ᇣ⊶䗚বᤶⱘ⚍ᗕᬊᬯᗻ,೼≵᳝؛ᅮߑ᭄ᰃᕘ৥ⱘᴵӊϟ,䅼䆎њdbSεf(x)=(Wψ1f)(a,b)τψ2(a,b)an+1daa>εRnⱘ޴Т໘໘ᬊᬯᗻ.៥Ӏⱘ㒧ᵰ᥼ᑓ੠ᬍ䖯њLi੠Sun[43]ҹঞWeisz[64]Ёⱘ䚼ߚ㒧ᵰ.ρ㄀ϝゴ,៥Ӏҟ㒡њᏺখ᭄ⱘMarcinkiewicz⿃ߚμㅫᄤ೼ࡴᴗHardyぎΩ䯈ⱘ᳝⬠ᗻ.߽⫼ࡴᴗHardyぎ䯈ⱘߚ㾷⧚䆎,ᓎゟњখ᭄ⱘMarcinkiewicz⿃ߚㅫᄤ೼ࡴᴗHardyぎ䯈,ࡴᴗᔅHardyぎ䯈ⱘ᳝⬠ᗻ,᥼ᑓњH

4、u੠Wang1ωq(δ)σ[21]ҹঞDing,Lu੠Xue[15]Ёⱘ㒧ᵰ,ᑊᇚᴵӊ(1+

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6、)dδ<∞,0δ1ωq(δ)σ>1ޣᔅЎ(1+

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8、)dδ<∞.0δ㄀ಯゴⷨおњHausdorffㅫᄤѸᤶᄤⱘ᳝⬠ᗻ.ᓎゟњᑓНHausdorffㅫᄤѸᤶᄤHΦ,β,Aⱘ᳝⬠ᗻ,ҹঞHausdorffㅫᄤϢCBMOߑ᭄⫳៤ⱘ໮㒓ᗻѸᤶᄤHf೼Lebesgueぎ䯈,Herzൟぎ䯈,Morrey-Herzൟぎ䯈ЁⱘΦ,β,b᳝⬠ᗻ.݊ЁHΦ,β,Af,HΦ,β,bfᅮН䆺㾕㄀ϔゴ㄀Ѡ㡖ᅮН.㄀Ѩゴ׳ࡽᵕ໻ߑ᭄ⷨおњḌ⒵䎇ᶤ⾡⿃ߚᴵӊⱘ໮㒓ᗻ༛ᓖ⿃ߚㅫᄤѸᤶᄤⱘࡴᴗ᳝⬠ᗻ.݇䬂䆡:ᇣ⊶বᤶ,

9、ᬊᬯᗻ,Marcinkiewicz⿃ߚ,Hausdorffㅫᄤ,໮㒓ᗻ༛ᓖ⿃ߚㅫᄤ,Ѹᤶᄤ,CBMOߑ᭄,Lipschitzߑ᭄,ᴗ,Hardyൟぎ䯈,ᔅHardyൟぎ䯈,Herzൟぎ䯈,Morrey-Herzൟぎ䯈.IABSTRACTThisPH.Dthesisfocusesonsomeproblemsabouttheboundednessandtheconvergenceofintegraloperator.Thepaperconsistsoffivechapters.InChapter1,weintroducesomefunctionspacesandsomerelevantoperato

10、rs.InChapter2,weconsiderthepointwiseconvergenceofinverseofnormalwavelettransform.Withouttheradialassumptionsonthewaveletfunctions,wediscussthefunctiondbSεf(x)=(Wψ1f)(a,b)τψ2(a,b)an+1daa>εRnisconvergentatalmosteverywherepoints.OurmaintheorempartlygeneralizeandimprovetheresultsofLiandSun[43],Weisz[

11、64].InChapter3,westudycharacteristicofParammetricMarcinkiewiczinte-gralsonHardyspaces.Byatomdecomposition,weobtaintheboundednessofρParammetricMarcinkiewiczintegralsμonweightedHardyandweakweightedΩHardyspace