FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 2, PAGES 565-581

On some maximal operators, connected with the operation of convolution

T. Y. Semenova

Abstract

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Some maximal operators, special cases of which include the maximal Hilbert operator and Hardy--Littlewood maximal function, have been considered in this article. We prove estimations that generalize Kolmogoroff and Riesz theorems under weaker conditions than in previous works of T. P. Lukashenko and M. Kotlyar.

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Last modified: September 1, 2000