CÁC BÀI BÁO KHOA HỌC 02:14:37 Ngày 11/07/2020 GMT+7
Maximal functions and weighted norm inequalities on local fields

Weight functions are characterized so that Hardy-Littlewood maximal operator is bounded in certain spaces. The reverse weak type estimates with applications to some singular integrals and to the class L(1+log+L) of Zygmund are established. These results are also compared with the ones in Euclidean case which are obtained by K.F. Andersen and W.S. Young, thereby showing the differences between the two cases. We introduce a weak type estimate for a new class of maximal function and employ it to deduce a special result on singular operators over a local field which is obtained by K. Phillips and M. Taibleson. © 2009 Elsevier Inc. All rights reserved.

 Chuong N.M., Hung H.D.
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  Từ khóa : Boundedness; Euclidean; Hardy-Littlewood maximal operators; Local fields; Phillips; Singular integral; Weak types; Weight functions; Weighted norm inequalities; Function evaluation; Fourier analysis