Lebesgue constants of Leja sequences: a universal lower bound and improved upper bounds on the real line

We prove a general lower bound for the Lebesgue constants $Λ_n$ of Leja sequences for every nonpolar compact set \(K\subset\mathbb C\): $\textstyle \limsup_{n \to+\infty} Λ_n \, \sqrt{n^{-1} W_n(K)}\geq \tfrac{1}{\sqrt{2}}$, where \(W_n(K)\) denotes the Chebyshev--Widom factor. In particular, bounde