A short proof of Stein's universal multiplier theorem

TL;DR

This paper presents a concise probabilistic proof of Stein's universal multiplier theorem, bypassing traditional harmonic analysis techniques such as complex interpolation and transference methods.

Contribution

It introduces a novel probabilistic approach to prove Stein's universal multiplier theorem, simplifying the proof process.

Findings

Proof is shorter and more accessible.

Avoids complex harmonic analysis methods.

Potential for broader applicability.

Abstract

We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).