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I am currently working on an analysis problem in fractional calculus and after some work I have encountered the following inequality: $$ |v(s)|~\leq \epsilon+\beta \int_{0}^{1}|s-x|^{\alpha-1}\left( |...

This question is post on MSE a week ago. I move it here to draw more attention. Let $u\in C^\infty(\bar I)$ be given where $I=(0,1)$. Define $$ t(\alpha):=\left(\int_I\int_I \frac{|u(x)-u(y)|^\alpha}{...