On the $L_p$ norm of the Rademacher projection and related inequalities

Abstract

Abstract. The purpose of this paper is to find the exact norm of the Rademacher projection onto {r 1 , r 2 , r 3 }. Namely, we prove

Sharp estimates for conditionally centred moments and for compact operators on $L^p$ spaces

“…This result was obtained originally in [34] for n = 2, 3, 4.) G. Lewicki and L. Skrzypek showed that c p in (11) tends to c p in (6) as n → ∞ and recovered C. Franchetti's result.…”

Sharp estimates for conditionally centered moments and for compact operators on Lp$L^p$ spaces

“…(If $$n = 3, 4$$, then the inequality $$\frac{k}{n} < \frac{1}{2}$$ means that $$k = 1$$, and (1.11) takes the form $$$$\begin{equation*} c_p = \frac{ {\left((n - 1)^{p - 1} + 1\right)}^{\frac{1}{p}} {\left((n - 1)^{\frac{1}{p - 1}} + 1\right)}^{1 - \frac{1}{p}}}{n}\, . \end{equation*}$$$$This result was obtained originally in [34] for $$n = 2, 3, 4$$.) G. Lewicki and L. Skrzypek showed that $$c_p$$ in (1.11) tends to $$c_p$$ in (1.6) as $$n \rightarrow \infty$$ and recovered C. Franchetti's result.…”

“…(see (1.7)), where This result was obtained originally in [34] for 𝑛 = 2, 3, 4.) G. Lewicki and L. Skrzypek showed that 𝑐 𝑝 in (1.11) tends to 𝑐 𝑝 in (1.6) as 𝑛 → ∞ and recovered C. Franchetti's result.…”