Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional ...Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional operators Ml with function b（x） in BMO（R^n）, respectively.展开更多
We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）...We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.展开更多
The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζ...The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζi（G） for all integer i or wi（G） = ζi＋1（G） for every integer i, and w（G/K） = ζ（G/K） for every normal subgroup g in G with K ≠ 1. Meanwhile, a necessary and sufficient condition for a regular p-group of maximal class satisfying w（G） = ζ2（G） is given. Finally, the authors prove that the power automorphism group PAut（G） is an elementary abelian p-group if G is a non-abelian p- group with elementary ζ（G） ∩ζ1（G）.展开更多
基金the National Natural Science Foundation of China(1057101410571158).
文摘Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional operators Ml with function b（x） in BMO（R^n）, respectively.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371295, 11471041 and 11526122)Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (Grant No. 2015RCJJ053)+2 种基金Research Award Fund for Outstanding Young Scientists of Shandong Province (Grant No. BS2015SF012)Outstanding Young Scientific and Technological Top-Notch Talents of College of Mathematics and Systems Science (Grant No. Sxy2016K01)Natural Science Foundation of Fujian Province of China (Grant No. 2015J01025)
文摘We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.
基金supported by the National Natural Science Foundation of China (No. 11071155)the Key Disciplines of Shanghai Municipality (No. S30104)
文摘The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζi（G） for all integer i or wi（G） = ζi＋1（G） for every integer i, and w（G/K） = ζ（G/K） for every normal subgroup g in G with K ≠ 1. Meanwhile, a necessary and sufficient condition for a regular p-group of maximal class satisfying w（G） = ζ2（G） is given. Finally, the authors prove that the power automorphism group PAut（G） is an elementary abelian p-group if G is a non-abelian p- group with elementary ζ（G） ∩ζ1（G）.
