Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2...Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.展开更多
Let 0 〈 a 〈 n, Ω be a rough kernel, and let A have derivatives of order m- 1 in CI3MOTM with m ≥ 2. We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type, and obtain the boundedness of TΩA...Let 0 〈 a 〈 n, Ω be a rough kernel, and let A have derivatives of order m- 1 in CI3MOTM with m ≥ 2. We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type, and obtain the boundedness of TΩA,α from the central Morrey spaces E^p,μ1 to E^r,λ for λ = μ1 ＋ μ2 ＋ α/n and 1/r = 1/p ＋ 1/q - α/n.展开更多
In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here...In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of L^s-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces.展开更多
基金Supported by National 973 Project(G.19990751)the SEDF of China(20040027001)
文摘Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.
基金supported by National Natural Science Foundation of China(Grant Nos.11226104 and 11226109)supported by National Natural Science Foundation of China(Grant Nos.11171306 and 11071065)Natural Science Foundation of Jiangxi Province(Grant No.20114BAB211007)
文摘Let 0 〈 a 〈 n, Ω be a rough kernel, and let A have derivatives of order m- 1 in CI3MOTM with m ≥ 2. We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type, and obtain the boundedness of TΩA,α from the central Morrey spaces E^p,μ1 to E^r,λ for λ = μ1 ＋ μ2 ＋ α/n and 1/r = 1/p ＋ 1/q - α/n.
基金Supported by the NNSF of China (Grant No.10871024)SEDF of China (Grant No.20040027001)
文摘In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of L^s-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces.
