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 Apr11 awarded Yearling Jul2 awarded Curious Jun23 awarded Organizer Jun23 comment An inequality between integrals of series of characteristic functions of cubes There was a very similar question answered here: math.stackexchange.com/questions/807426/… I would like to know if one could do this for $p<1$ Jun23 revised An inequality between integrals of series of characteristic functions of cubes harmonic analysis is more appropriate here than just "analysis" Jun23 suggested approved edit on An inequality between integrals of series of characteristic functions of cubes May15 answered An analysis qual problem Apr11 awarded Yearling Mar16 comment Prove that the Laplacian of the integral of a certain function is $0$ This is essentially the Poisson extension: en.wikipedia.org/wiki/Poisson_kernel Mar16 comment Prove that the Laplacian of the integral of a certain function is $0$ Are you missing a $y$ on the numerator? Feb16 comment For what values of $p>0, \quad \int^{1}_{0} \frac{x}{\sin{(x^{p})}} \operatorname d\!x$ converges? There isn't any oscillation near $0$ to prevent the integral to blowing up as you make $t$ apporach $0$. So my guess is that this exists whenever $0< p <2$ and diverges for all $p \geq 2$. That this blows up for $p\geq 2$ can easily be proved using the estimate $\sin(x) \leq x$. That it converges for $00$. Can you show your work?