奥立兹类中单边哈代-利特尔伍德最大函数的加权弱式不等式的统一版本

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-11 DOI:10.3390/math12182814

Erxin Zhang

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引用次数: 0

摘要

设 Mg+f 为单边哈代-利特尔伍德最大函数，φ1 为定义在 [0,∞) 上的非负且非递减函数，γ 为定义在 [0,∞) 上的正且非递减函数；设φ2 为准凸函数，u,v,w 为三个权函数。本文提出了权重函数（u,v,w）的必要条件和充分条件，使得不等式φ1(λ)∫{Mg+f>λ}u(x)g(x)dx≤C∫-∞+∞φ2(C|f(x)|v(x)γ(λ))w(x)g(x)dx 成立。然后，我们把弱型和超弱型单边哈代-利特尔伍德最大不等式统一到上述不等式中。

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A Unified Version of Weighted Weak-Type Inequalities for the One-Sided Hardy–Littlewood Maximal Function in Orlicz Classes

Let Mg+f be the one-sided Hardy–Littlewood maximal function, φ1 be a nonnegative and nondecreasing function on [0,∞), γ be a positive and nondecreasing function defined on [0,∞); let φ2 be a quasi-convex function and u,v,w be three weight functions. In this paper, we present necessary and sufficient conditions on weight functions (u,v,w) such that the inequality φ1(λ)∫{Mg+f>λ}u(x)g(x)dx≤C∫−∞+∞φ2(C|f(x)|v(x)γ(λ))w(x)g(x)dx holds. Then, we unify the weak and extra-weak-type one-sided Hardy–Littlewood maximal inequalities in the above inequality.

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来源期刊

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.