变量核齐次分数次积分在Morrey空间上的估计
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摘要
利用空间分解技术和核函数估计,在核函数满足一定的Ls-Dini条件下,得到了变量核齐次分数次积分TΩ,α是从Morrey空间Lλ/α,λ(Rn)到BMO(Rn)上的有界算子,同时从Lp,λ(Rn)到Campanato空间fl,n(α/n-λ/np)(Rn)也是有界的.
Using partial decomposition technique and kernel function estimation,under some Ls-Dini conditions of the kernel functions,we obtain that the homogeneous fractional integral operator with the variable λ,kernel TΩ,αis bounded from the Morrey spaces Lλ/α,λ(Rn)to BMO(Rn),and also from Lp,λ(R~n)to a class of the Campanato spaces fl,n(α/n-λ/np)(R~n).
Using partial decomposition technique and kernel function estimation,under some Ls-Dini conditions of the kernel functions,we obtain that the homogeneous fractional integral operator with the variable λ,kernel TΩ,αis bounded from the Morrey spaces Lλ/α,λ(Rn)to BMO(Rn),and also from Lp,λ(R~n)to a class of the Campanato spaces fl,n(α/n-λ/np)(R~n).
引文
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[2]FAZIO G D,RAGUSA M A.Interior Estimates in Morrey Spaces for Strong Solutions to Nondivergence form Equations with Discontinuous Coefficients[J].J Func Anal,1993,112(2):241-256.
[3]CALDERN A P,ZYGMUND A.On Singular Integrals with Variable Kernels[J].Appl Anal,1978,7(3):221-238.
[4]DING Y,LIN C C,SHAO S.On Marcinkiewicz Integral with Variable Kernels[J].Indiana Univ Math J,2004,53(3):805-821.
[5]CHEN Y P,DING Y,LI R.The Boundedness for Commutator of Fractional Integral Operator with Rough Variable Kernel[J].Potential Anal,2013,38(1):119-142.
[6]陶双平,邵旭馗.带变量核的Marcinkiewicz积分在齐次Morrey-Herz空间上的有界性[J].兰州大学学报(自然科学版),2010,46(3):102-107.
[7]李睿,陶双平.多线性奇异积分算子在加权Morrey-Herz空间上的有界性[J].西南大学学报(自然科学版),2016,38(10):62-67.
[8]陶双平,龚少花,温学平.广义Hausdorff算子的加权lipschitz估计[J].西南大学学报(自然科学版),2014,36(6):111-115.
[9]ADAMS D R.A Note on Riesz Potentials[J].Duke Matn J,1975,42(4):765-778.
[10]DING Y,LU S.Boundedness of Homogeneous Fractional Integrals on Lp for n/α≤p≤∞[J].Nagoya Mathematical Journal,2002,167(2002):17-33.
[11]MENG S Y,CHEN Y P.Boundedness of Homogeneous Fractional Integral Operator on Morrey Space[J].J.Inequal.Appl,2016,2016(1):1-11.