##  [Hardy Space](/hardy-space) 

  ##  [Hardy Space](https://puremath.quantumdictionary.io/hardy-space-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A class of function spaces H^p of holomorphic functions (on the unit disc or upper half-plane) or of boundary distributions on R^n (real Hardy spaces) with controlled p-norm growth or atomic decompositions; fundamental in complex analysis and harmonic analysis as replacements for L^p at endpoints.