##  [Littlewood–Paley Theory](/index.php/littlewood-paley-theory) 

  ##  [Littlewood–Paley Theory](https://puremath.quantumdictionary.io/littlewood-paley-theory-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A collection of techniques and decompositions based on frequency localization (dyadic partitions of unity, Littlewood–Paley projections) that analyze function-space regularity and produce square-function and norm equivalences central to harmonic analysis and PDE estimates.