两极分化的哈代斯坦身份

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-01-13 DOI:10.1016/j.jfa.2025.110827

Krzysztof Bogdan , Michał Gutowski , Katarzyna Pietruska-Pałuba

引用次数: 0

摘要

证明了Lp（Rd;Rn）上具有1<；p<；∞的向量函数和Lp（Rd）上具有2≤p<；∞的两个实数函数的正则配对的Hardy-Stein恒等式。为此，我们提出了布雷格曼共散度的概念，并研究了相应的积分形式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Polarized Hardy–Stein identity

We prove the Hardy–Stein identity for vector functions in

L^{p} (R^{d}; R^{n})

with

1 < p < \infty

and for the canonical paring of two real functions in

L^{p} (R^{d})

with

2 \leq p < \infty

. To this end we propose a notion of Bregman co-divergence and study the corresponding integral forms.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis