On fractional Orlicz-Hardy inequalities

IF 1.2 3区 数学 Q1 MATHEMATICS
T.V. Anoop , Prosenjit Roy , Subhajit Roy
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引用次数: 0

Abstract

We establish the weighted fractional Orlicz-Hardy inequalities for various Young functions satisfying the 2-condition. Further, we identify the critical cases for such Young 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 Young function Φ satisfying the 2-condition and for any Λ>1, the following inequality is establishedΦ(a+b)λΦ(a)+C(Φ,Λ)(λ1)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.
关于分数奥立兹-哈代不等式
我们为满足△2 条件的各种杨函数建立了加权分数奥立兹-哈代不等式。此外,我们还确定了此类杨函数的临界情况,并证明了带对数修正的加权分数奥立兹-哈代不等式。此外,我们还讨论了局部情况下的类似结果。在此过程中,对于满足△2 条件的任意 Young 函数 Φ 和任意Λ>1,建立了以下不等式Φ(a+b)≤λΦ(a)+C(Φ,Λ)(λ-1)Φ+-1Φ(b),∀a,b∈[0,∞),∀λ∈(1,Λ],其中Φ+:=sup{tΦ(t)/Φ(t):t>0},Φ是Φ的右导数,C(Φ,Λ)是只取决于Φ和Λ的正常数。
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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