多线性分数次积分算子的交换子在Herz型空间上的有界性
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摘要
利用Minkowski不等式、Hlder不等式及一些泛函分析技巧,证明了由分数次积分算子Il和Lipschitz函数生成的多线性交换子[b,Il]在Herz空间与Morrey-Herz空间上的有界性.
The boundedness of the multilinear commutators [b,Il] generated by the fractional integral operators Iland Lipschitz function on Herz spaces and Morrey-Herz spaces are proved by using the Minkowski inequality,the Hlder inequality and some method of functional analysis.
The boundedness of the multilinear commutators [b,Il] generated by the fractional integral operators Iland Lipschitz function on Herz spaces and Morrey-Herz spaces are proved by using the Minkowski inequality,the Hlder inequality and some method of functional analysis.
引文
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[10]SHIRAI S.Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces[J].Kokkaido Math J,2006,35(3):683-696.
[2]STEIN E M,WEISS G.Introduction to Fourier analysis on Euclidean spaces[M].Princeton:Princeton University Press,1971.
[3]薛丽梅,郭景芳,侯常兴.一类多线性奇异积分算子的端点估计[J].河北师范大学学报:自然科学版,2011,35(1):13-16.
[4]GRAFAKOS L.On multilinear fractional integrals[J].Studia Math,1992,102(1):49-56.
[5]STEIN E M.Singular integrals and differentiability properties of functions[M].Princeton:Princeton University Press,1970.
[6]JANSON S.Mean oscillation and commutators of singular integral operators[J].Ark Math,1978,16(2):263-270.
[7]PEETRE J.On the theory of Lp,λspaces[J].J Funct Anal,1969,4(1):71-87.
[8]ADAMS D R.A note on Riesz potentials[J].Duke Math J,1975,42(4):765-778.
[9]LU S Z,YANG D C.Hardy-Littlewood-Sobolev theorems of fractional integration on Herz-type spaces and its applications[J].Can J Math,1996,48(2):363-380.
[10]SHIRAI S.Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces[J].Kokkaido Math J,2006,35(3):683-696.