On general Caffarelli-Kohn-Nirenberg type inequalities involving non-doubling weights in the case of p=1

2025/12/25 by Toshio Horiuchi, Horiuchi, Toshio
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35J70 #Secondary 35J60 #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2512.21492

openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

We study the Caffarelli-Kohn-Nirenberg type inequalities in the case of p=1 and generalize them adopting weight functions w(|x|) on Rⁿ with w(t) in W(R₊). Here W(R₊) is a general class of weight functions on R₊ including non-doubling weights like e^1/t and e^-1/t.

Citations

• Generalized weighted Hardy's inequalities with compact perturbations
• Hardy's inequalities with non-doubling weights and sharp remainders

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