On Fractional Orlicz-Hardy Inequalities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909116457287680 |
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| author | Anoop, T. V. Roy, Prosenjit Roy, Subhajit |
| author_facet | Anoop, T. V. Roy, Prosenjit Roy, Subhajit |
| contents | 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 $$
Φ(a+b)\leq λΦ(a)+\frac{C(
Φ, Λ
)}{(λ-1)^{p_Φ^+-1}}Φ(b),\;\;\;\forall\,a,b\in [0,\infty),\,\forall\,λ\in (1,Λ], $$
where $p_Φ^+:=\sup\big\{tφ(t)/Φ(t):t>0\big\},$ $φ$ is the right derivatives of $Φ$ and $C(
Φ, Λ
)$ is a positive constant that depends only on $Φ$ and $Λ.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Fractional Orlicz-Hardy Inequalities Anoop, T. V. Roy, Prosenjit Roy, Subhajit Analysis of PDEs 46E30, 35R11, 35A23 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 $$ Φ(a+b)\leq λΦ(a)+\frac{C( Φ, Λ )}{(λ-1)^{p_Φ^+-1}}Φ(b),\;\;\;\forall\,a,b\in [0,\infty),\,\forall\,λ\in (1,Λ], $$ where $p_Φ^+:=\sup\big\{tφ(t)/Φ(t):t>0\big\},$ $φ$ is the right derivatives of $Φ$ and $C( Φ, Λ )$ is a positive constant that depends only on $Φ$ and $Λ.$ |
| title | On Fractional Orlicz-Hardy Inequalities |
| topic | Analysis of PDEs 46E30, 35R11, 35A23 |
| url | https://arxiv.org/abs/2401.06434 |