Sharp singular Adams inequalities in high order Sobolev spaces

2011/12/29 by Nguyen Lam, Guozhen Lu, Lam, Nguyen +1 · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1112.6431

openalex publication_date 2011/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in ℝⁿ. Using this we prove a sharp singular Adams inequality in high order Sobolev spaces in bounded domain at critical case. Then we prove sharp singular Adams inequalities for high order derivatives on unbounded domains. Our results extend the singular Moser-Trudinger inequalities of first order in \citeAd2, R, LR, AdY to the higher order Sobolev spaces W^m,(n)/(m) and the results of \citeRS on Adams type inequalities in unbounded domains to singular case. Our singular Adams inequality on W^2,2(ℝ⁴) with standard Sobolev norm at the critical case settles a unsolved question remained in \citeY.

Citations

• Trudinger type inequalities in 𝐑^𝐍 and their best exponents

Cited by

• The singular anisotropic Adams' type inequality in ℝⁿ

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