2024/01/12 by T. V. Anoop, Anoop, T. V., Prosenjit Roy +3 · 1 citation
Mathematics · #35A23 #35R11 #46E30 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2401.06434
openalex publication_date 2024/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish the weighted fractional Orlicz-Hardy inequalities for various Orlicz functions. Further, we identify the critical cases for each Orlicz function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic correction. Moreover, we discuss the analogous results in the local case. In the process, for any Orlicz function Φ and for any Λ>1, the following inequality is established Φ(a+b)≤ λΦ(a)+\fracC( Φ, Λ )(λ-1)pΦ+-1Φ(b), ∀ a,b∈ [0,∞), ∀ λ∈ (1,Λ], where pΦ+:=sup\tφ(t)/Φ(t):t>0\, φ is the right derivatives of Φ and C( Φ, Λ ) is a positive constant that depends only on Φ and Λ.