ABSTRACT
Rademacher-Men’ˇsov Inequality If φk : [0, 1] 7→ C, 1 ≤ k ≤ n, are orthonormal and if ck ∈ C, 1 ≤ k ≤ n, then:∫ 1
max 1≤k≤n
∣∣∣∣( k∑ j=1
cjφj(x) )2∣∣∣∣ dx ≤ log22(4n) n∑
|cj |2.
Comments (i) This result, found independently and almost at the same time by the two mathematicians named, is one of the most important in the study of the summability of orthonormal series. (ii) An interesting discussion of this result appears in the paper by Mo´ricz.
