ABSTRACT
Kaczmarz & Steinhaus Inequalities If p > 2 then for some constant α depending only on p,
|1 + x|p ≤ 1 + px+ [p]∑ i=2
( p
i
) xi + α|x|p, x ∈ R.
Corollary If p > 2 and f, g ∈ Lp([a, b]) then there are constants α, β depending only on p such that
|f + g|p ≤ ∫ b a
|f |p + p ∫ b a
|f |p−2fg + α ∫ b a
|g|p + β [p]∑ i=2
|f |p−1|g|i.
