Littlewood, Paley and Almost-Orthogonality: a theory well ahead of its time

TL;DR

This paper reviews the historical development and significance of Littlewood--Paley theory, highlighting its early insights and influence on modern harmonic analysis over the past century.

Contribution

It provides a historical analysis of Littlewood--Paley theory, emphasizing its ahead-of-its-time insights and its impact on subsequent mathematical developments.

Findings

Historical importance of Littlewood--Paley theory

Influence on modern harmonic analysis

Early insights that shaped future research

Abstract

Littlewood--Paley theory began with the classic paper of Littlewood and Paley (J.\ E.\ Littlewood, R.\ E.\ A.\ C.\ Paley, {\em Theorems on Fourier Series and Power Series}. J. Lond. Math. Soc. (1), {\bf 6} (1931), 230--33). We discuss this paper and its impact from a historical perspective. We include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them into the context of the current state of the art in harmonic analysis and beyond.