A new look at subrepresentation formulas

2024/06/19 by Cong Hoang, Kabe Moen, Hoang, Cong +3 · 1 citation
Economics, Econometrics and Finance · Decision Sciences · Computer Science · #Game Theory and Voting Systems #Multi-Criteria Decision Making #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2406.13772

Abstract

We extend the subrepresentation formula |f(x)|≤ c_n I₁(|∇ f|)(x) in several ways. First, we consider more general A₁-potential operators on the right-hand side and prove local and global pointwise inequalities for these operators. Second, we show that we can improve the right-hand side using fractional derivatives. Finally, we extend our results to rough singular integral operators, similar to the main result in [HMP1].

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• New weighted Riesz-type pointwise inequalities and applications to generalized Sobolev estimates

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