Degenerate Poincaré-Sobolev inequalities via fractional integration

IF 1.6 2区 数学 Q1 MATHEMATICS
Alejandro Claros
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引用次数: 0

Abstract

We present a local weighted estimate for the Riesz potential in Rn, which improves the main theorem of Alberico et al. (2009) [2] in several ways. As a consequence, we derive weighted Poincaré-Sobolev inequalities with sharp dependence on the constants. We answer positively to a conjecture proposed by Pérez and Rela (2019) [36] related to the sharp exponent in the A1 constant in the (p,p) Poincaré-Sobolev inequality with A1 weights. Our approach is versatile enough to prove Poincaré-Sobolev inequalities for high-order derivatives and fractional Poincaré-Sobolev inequalities with the BBM extra gain factor (1δ)1p. In particular, we improve one of the main results from Hurri-Syrjänen et al. (2023) [24].
通过分数积分退化poincar sobolev不等式
我们提出了Rn中Riesz势的局部加权估计,它从几个方面改进了Alberico et al.(2009)[2]的主要定理。因此,我们导出了对常数有明显依赖的加权poincar - sobolev不等式。我们肯定地回答了p和Rela(2019)[36]提出的一个猜想,该猜想与(p,p) poincar - sobolev不等式中A1常数的急剧指数具有A1权重。我们的方法是通用的,足以证明高阶导数的poincar - sobolev不等式和带有BBM额外增益因子(1−δ)1p的分数poincar - sobolev不等式。特别是,我们改进了Hurri-Syrjänen等人(2023)[24]的主要结果之一。
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来源期刊
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
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