Hardy space
In complex analysis, the Hardy spaces (or Hardy classes) "Hp" are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real analysis Hardy spaces are certain spaces of distributions on the real line, which are (in the sense of distributions) boundary values of the holomorphic functions of the complex Hardy spaces, and are related to the "Lp" spaces of functional analysis. For 1 ≤ "p" ≤ ∞ these real Hardy spaces "Hp" are certain subsets of "Lp", while for "p" < 1 the "Lp" spaces have some undesirable properties, and the Hardy spaces are much better behaved.

There are also higher-dimensional generalizations, consisting of certain holomorphic functions on tube domains in the complex case, or certain spaces of distributions on R"n" in the real case.

Hardy spaces have a number of applications in mathematical analysis itself, as well as in control theory (such as "H"∞ methods) and in scattering theory.
Q193756
complex analysis
Concept
Q472971
spaces
Concept
Q207476
holomorphic function
Concept
Q2390323
unit disk
Concept
Q3258885
upper half plane
Concept
Q380366
Frigyes Riesz
PER
Q184337
G. H. Hardy
PER
Q854531
real analysis
Concept
Q865811
distributions
Concept
Q11567
complex
Concept
Q305936
"Lp" spaces
Concept
Q190549
functional analysis
Concept
Q177646
subset
Concept
Q17104332
tube domain
UNK
Q7754
mathematical analysis
Concept
Q6501221
control theory
Concept
Q1293742
"H"∞ methods
UNK
Q903737
scattering theory
UNK
Q1585233
Hardy space
Concept
Q1585233
Hardy space
Concept
Q1585233
Hardy space
Concept
Q1585233
Hardy space
Concept
Q1585233
Hardy space
Concept
Q1585233
Hardy space
Concept
+1^^http://www.w3.org/2001/XMLSchema#decimal
1
NUMBER
+1^^http://www.w3.org/2001/XMLSchema#decimal
1
NUMBER
discoverer or inventor
named after
studies