A Bound on the Difference between the Chebyshev Norm and the Hölder Norms of a Function
M. D. Hebden · SIAM Journal on Numerical Analysis · 1971
By restricting the class of functions considered and by following a similar approach to that used when the domain is a finite point set, it is shown that, for a function defined on a continuum and satisfying a Lipschitz condition, the $L_p $-norm approaches the Chebyshev norm at the rate $p^{ - 1} \log p$ as the index p becomes infinite.