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Boundary fractional Hardy's inequality in dimension one: The critical case

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arxiv 2407.12098 v1 pith:WVZUKZES submitted 2024-07-16 math.AP

Adimurthi , Purbita Jana , Prosenjit Roy This is my paper · ORCID
classification math.AP
keywords inequalityboundarycasecriticaldimensionfractionalhardyappears
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abstract

We prove fractional boundary Hardy's inequality in dimension one for the critical case $sp =1$. Optimality of the inequality is obtained for any $p$. The extra logarithmic correction term appears in usual fashion. We also provide a concrete (workable) example of a sequence of smooth functions that converges to constant function in $W^{s,p}((0,1))$ for $sp=1$ and $p=2$.

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