简介:<正>Let{Ei:i∈I}beafamilyofArchimedeanRieszspaces.TheRieszproductspaceisdenotedbyΠi∈IEi.Themainresultinthispaperisthefollowingconclusion:ThereexistsacompletelyregularHausdorffspaceXsuchthatΠi∈IEiisRieszisomorphictoC(X)ifandonlyifforeveryi∈IthereexistsacompletelyregularHausdorffspaceXisuchthatEiisRieszisomorphictoC(Xi).
简介:在这篇论文,我们认为Riesz产品dμ=Π_(j=1)~∞(是1+a_jReχ_(b_(jp)λ_j)(x))dx在本地人地,和我们获得它的Hausdorffdimension的上面、更低的界限。
简介:LetL=-△+VbeaSchrodingeroperatoronRn(n≥3),wherethenon-negativepotentialVbelongstoreverseHolderclassRHq1forq1>n/2.LetHLp(Rn)betheHardyspaceassociatedwithL.Inthispaper,weconsiderthecommutator[b,Tα],whichassociatedwiththeRiesztransformTα=Vα(-?+V)-αwith0<α≤1,andalocallyintegrablefunctionbbelongstothenewCampanatospaceΛβθ(ρ).Weestablishtheboundednessof[b,Tα]fromLp(Rn)toLq(Rn)for1
简介:AsequenceofsphericalzonaltranslationnetworksbasedontheBochner-RieszmeansofsphericalharmonicsandtheRieszmeansofJacobipolynomialsisintroduced,anditsdegreeofapproximationisachieved.Theresultsobtainedinthepresentpaperactuallyimplythattheapproximationofzonaltranslationnetworksisconvergentiftheactionfunctionshavecertainsmoothness.
简介:LetL=-?+VbeaSchrdingeroperatoractingonL2(Rn),n≥1,whereV≡0isanonnegativelocallyintegrablefunctiononRn.Inthisarticle,wewillintropduceweightedHardyspacesHL(w)associatedwithLbymeansofthesquarefunctionandthenstudytheiratomicdecompositiontheory.WewillalsoshowthattheRiesztransform?L-1/2associatedwithLisboundedfromournewspaceHpL(w)totheclassicalweightedHardyspaceHp(w)whenn/(n+1)
简介:Inthispaper,weconsiderthealmosteverywhereconvergencofBochner-RieszmeansbelowthecriticalindexinBesselpotentialspacesanda>0)andfindouttherelationbetweentheindexofBochner-Rieszmeansandthedegreeofsmoothnessoffunctions.
简介:Inthispaper,weconsideraRieszspace-fractionalreaction-dispersionequation(RSFRDE).TheRSFRDEisobtainedfromtheclassicalreaction-dispersionequationbyreplacingthesecond-orderspacederivativewithaRieszderivativeoforderβ∈(1,2].WeproposeanimplicitfinitedifferenceapproximationforRSFRDE.Thestabilityandconvergenceofthefinitedifferenceapproximationsareanalyzed.Numericalresultsarefoundingoodagreementwiththetheoreticalanalysis.
简介:Inthispaper,thespace-timeRieszfractionalpartialdifferentialequationswithperiodicconditionsareconsidered.TheequationsareobtainedfromtheintegralpartialdifferentialequationbyreplacingthetimederivativewithaCaputofractionalderivativeandthespacederivativewithRieszpotential.ThefundamentalsolutionsofthespaceRieszfractionalpartialdifferentialequation(SRFPDE)andthespace-timeRieszfractionalpartialdifferentialequation(STRFPDE)arediscussed,respectively.UsingmethodsofFourierseriesexpansionandLaplacetransform,wederivetheexplicitexpressionsofthefundamentalsolutionsfortheSRFPDEandtheSTRFPDE,respectively.
简介:本文中,我们研究一类由极大Bochner—Riesz算子和Lipschtz函数A生成的多线性算子,获得了它的(Lp,上q)型,而且我们还将证明此算子从Lebesgue空间到Lipschtz空间、从Herz空间到Campanato空间和从Lp空间到Tribel—Lizorkin空间的有界性.