An inverse Sidon type inequality for the Walsh system
Sidon inequalities, upper estimates of integral norms of Dirichlet kernels, have a long and interesting history whose latest chapter began with the paper by \textit{R. Bojanić} and \textit{C. V. Stanojević} [Trans. Am. Math. Soc. 269, 677-683 (1982; Zbl 0493.42011)]. Although each paper tended to offer some small improvement over one of its predecessors, no one had given serious consideration to where all this would end. In this paper, the author addresses this question head on by obtaining both upper and lower estimates. The result is the best rearrangement invariant expression of coefficients for a Sidon type inequality. (The expression itself, which bristles with technicalities involving \(\log^+\) of ratios of partial sums, can be associated with an Orlicz norm.) In addition to presenting interesting results, the paper also contains many remarks which bring out the history as well as the applications of Sidon inequalities. It is both well written and informative.
scientific article; zbMATH DE number 811200