摘要
该文定义了一类极大算子:角向H-L极大算子,如M_1^+f(x)=sup k>01/h^n integral from x_1 to x_1+k…integral from x_1 to x_1+k|f(x)|dt,?x=(x_1,…x_n)∈R^n。对于任一权W,该文得到存在另一非平凡权V,使得‖M_1^+F‖_J(V)≤C‖f‖J(W)的充要条件,同时得到这种类型的其它极大算子的相应结果。文中还获得了强极大算子在加权Lorentz空间上有界的充要条件。
This paper defines a kind of maximal operators, i. e. Angular-oriented H-L maximal operators,for example,|f(t) |dt,? x = (x_1,…,x_n) ∈R^n. For a weight W, a necessary and suffi-cient condition is obtained for the existence of a nontrivial weight V such that||M_1+ f||_(L?(V))≤ C||f||_(L?(W)). At the same time,this paper obtains the corre-sponding result for other maximal operators of this kind. The paper also ob-tains a necessary and sufficient condition for the boundedness of strong maxi-mal operator on weighted Lorentz space L_W (p,q).
关键词
算子
权
范数
不等式
算子代数
Operator
weight
norm
inequality
operator algebra
Lorentz space
