珀尔森-斯特帕诺夫定理

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-07-09 DOI:10.1007/s13324-025-01102-5

Amiran Gogatishvili, Luboš Pick, Hana Turčinová, Tuğçe Ünver

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引用次数: 0

摘要

我们提出了l - e结果的一个新的证明。Persson和V.D. Stepanov[24，定理1和定理3]，它提供了涉及两个权重的Hardy积分不等式的表征，并且可以应用于几何平均算子的有效处理。我们的方法使我们能够将他们的结果扩展到所有参数范围，特别是涉及临界情况\(p=1\)，这在原始工作中被排除在外。我们的证明避免了所有的对偶步骤和离散化技术，只使用了基本的方法。

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The Persson–Stepanov theorem revisited

We develop a new proof of the result of L.-E. Persson and V.D. Stepanov [24, Theorems 1 and 3], which provides a characterization of a Hardy integral inequality involving two weights, and which can be applied to an effective treatment of the geometric mean operator. Our approach enables us to extend their result to the full range of parameters, in particular involving the critical case \(p=1\), which was excluded in the original work. Our proof avoids all duality steps and discretization techniques and uses solely elementary means.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.