Here $p, q$ denote conjugate exponents. Essentially, what problems were (I assume Riesz) and other's working on that made them realize this connection? Were there example functions they found that hinted this may be true?
The following question gives a strong motivation for Holders: Geometric interpretation of Young's inequality
And from Holder's I can see that we can associate $L^q$ with some set of linear functionals on $L^p$. But from here, it doesn't seem intuitive to me that all bounded linear functionals are determined by $L^q$.
