In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for cl...In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.展开更多
For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= （y1, Y2,…, ym） and 7 denotes the m-tuple （f1, f2,…, fm）. In this note, the one- weighted and ...For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= （y1, Y2,…, ym） and 7 denotes the m-tuple （f1, f2,…, fm）. In this note, the one- weighted and two-weighted boundedness on Lp （JRn） space for multilinear fractional integral operator I（am） and the fractional multi-sublinear maximal operator Mα（m） are established re- spectively. The authors also obtain two-weighted weak type estimate for the operator Mα（m）.展开更多
Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα...Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights.展开更多
Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results an...Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos[2].展开更多
In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.
Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights f...Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.展开更多
Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Mor...Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Morrey spaces and Lipschitz spaces associated with it, which, in the case when μ is the d-dimensional Lebesgue measure, also improve the known results.展开更多
The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO funct...In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space.Moreover,we give an endpoint estimate for multilinear fractional integral operators.As an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.展开更多
基金Supported by the National Natural Sciences Foundation of China (10771110)the Natural Science Founda- tion of Ningbo City (2006A610090)
文摘In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.
基金the NNSF of China under Grant#10771110NSF of Ningbo City under Grant#2006A610090
文摘For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= （y1, Y2,…, ym） and 7 denotes the m-tuple （f1, f2,…, fm）. In this note, the one- weighted and two-weighted boundedness on Lp （JRn） space for multilinear fractional integral operator I（am） and the fractional multi-sublinear maximal operator Mα（m） are established re- spectively. The authors also obtain two-weighted weak type estimate for the operator Mα（m）.
文摘Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights.
文摘Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos[2].
基金supported financially by Grant-in-Aid for Young Scientists (B) (Grant No. 21740104), Japan Society for the Promotion of Science
文摘In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.
基金National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.
基金Supported by the National Natural Science Foundation of China(No.10871025)
文摘Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Morrey spaces and Lipschitz spaces associated with it, which, in the case when μ is the d-dimensional Lebesgue measure, also improve the known results.
基金Supported by Zhejiang Provincial Natural Science Foundation of China under Grant (No.M103069)supported by the Education Dept. of Zhejiang Province(20021022)
文摘The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
基金supported by National Natural Science Foundation of China(11871452,12071473)the Beijing Information Science and Technology University Foundation(2025031)。
文摘In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space.Moreover,we give an endpoint estimate for multilinear fractional integral operators.As an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.
基金supported by the National Natural Science Foundation of China(Nos.11271330,11261023,11461033,11401269)the Jiangxi Provincial Natural Science Foundation of China(No.20142BAB201003)
文摘In this paper, some endpoint estimates for the generalized multilinear fractional integrals Ia,m on the non-homogeneous metric spaces are established.
