On fractional maximal function and fractional integrals associated with the Dunkl operator on the real line

In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the Dunkl-type fractional maximal operator Mβ, and the Dunkl-type fractional integral operator Iβ from the spaces Lp,α(R) to the spaces Lq,α(R), 1<p<q<∞, and from the spaces L1,α(R) to the weak spaces WLq,α(R), 1<q<∞. In the case , we prove that the operator Mβ is bounded from the space Lp,α(R) to the space L∞,α(R), and the Dunkl-type modified fractional integral operator is bounded from the space Lp,α(R) to the Dunkl-type BMO space BMOα(R). By this results we get boundedness of the operators Mβ and Iβ from the Dunkl-type Besov spaces to the spaces , 1<p<q<∞, 1/p−1/q=β/(2α+2), 1?θ?∞ and 0<s<1.     

Hardy-Littlewood最大算子的两个推广

§1IntroductionHardy-Littlewood maximal operator has wide applications in many fields,such asquasiconformal analysis,partial differential equations(PDEs)and harmonic analysis.LetΩbe an open subset of Rn,the Hardy-Littlewood maximal operator is defined on Ll1oc(Ω)by the ruleMh(x)=MΩh(x)=sup∫-B(x,t)h(y)dy:0相似文献   

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加权Morrey空间上分数次极大算子的双权不等式

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分数次Orlicz极大算子在齐型空间中的局部加权端点估计

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On the invariance of maximal distributional chaos under an annihilation operator

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On certain subclasses of multivalent functions associated with an extended fractional differintegral operator

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Weighted estimates for commutators of singular integral operators with non-doubling measures

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On a conformal invariant of the dirac operator on noncompact manifolds

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On certain conjectures on invariant measures on semigroups

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Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

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Isometries of certain operator spaces

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Weighted endpoint estimates for maximal commutators associated with the sections

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On fractional maximal function and fractional integral on the Laguerre hypergroup

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