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Jul 4, 2014 at 4:50 comment added Christian Remling @AthanagorWurlitzer: No problem, of course. As for the remaining case, I don't really have a good idea right now, but I have a feeling that one has to study $f$ near $b$ rather carefully; just Holder feels too "soft."
Jul 3, 2014 at 16:48 comment added Christian Remling @AthanagorWurlitzer: I don't think restricting to a subinterval will work since $\|f\|_{L^p(c,d)}<\|f\|_{L^p(a,b)}$, so the restricted $f$ will no longer satisfy the equation you're trying to solve.
Jul 3, 2014 at 10:46 comment added username Considering continuous functions on $(a,b)$ (as they must be), you excluded all cases, $b-a>1$, $b-a=1$ and $b-a<1$. The interval being bounded, can't you remove the last case by just considering $(c,d)\subset(a,b)$?
Jul 3, 2014 at 5:13 history edited Christian Remling CC BY-SA 3.0
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Jul 3, 2014 at 5:08 history edited Christian Remling CC BY-SA 3.0
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Jul 2, 2014 at 23:48 history answered Christian Remling CC BY-SA 3.0