Carleson measure
E943110
A Carleson measure is a type of measure in harmonic analysis that characterizes boundary behavior and embedding properties of function spaces such as Hardy and BMO spaces.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Carleson measure canonical | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
measure in harmonic analysis ⓘ |
| appliesTo |
analytic functions
ⓘ
harmonic functions ⓘ solutions of elliptic partial differential equations ⓘ |
| characterizes |
boundary behavior of functions
ⓘ
embedding properties of function spaces ⓘ |
| definedOn |
domains in C^n
ⓘ
unit ball in C^n ⓘ unit disk ⓘ upper half-plane ⓘ |
| field |
complex analysis
ⓘ
functional analysis ⓘ harmonic analysis ⓘ |
| generalizationOf | Muckenhoupt A_p weight condition in some settings ⓘ |
| hasCharacterization | supremum over boundary intervals of normalized measure of associated Carleson regions is finite ⓘ |
| hasCondition |
Carleson box condition
ⓘ
Carleson square condition ⓘ Carleson tent condition ⓘ |
| hasVariant |
Carleson measure on trees
ⓘ
operator-valued Carleson measure ⓘ vector-valued Carleson measure ⓘ |
| implies |
bounded embedding of BMOA into L^1(mu)
ⓘ
bounded embedding of Hardy space H^p into L^p(mu) ⓘ |
| namedAfter | Lennart Carleson NERFINISHED ⓘ |
| relatedTo |
BMO space
ⓘ
Bergman space NERFINISHED ⓘ Carleson embedding theorem NERFINISHED ⓘ Carleson interpolation theorem NERFINISHED ⓘ Corona theorem NERFINISHED ⓘ Dirichlet space NERFINISHED ⓘ Hardy space NERFINISHED ⓘ boundary values of analytic functions ⓘ logarithmic Carleson measure ⓘ non-tangential convergence of harmonic functions ⓘ parabolic Carleson measure ⓘ vanishing Carleson measure ⓘ |
| usedFor |
characterizing boundedness of Hankel operators
ⓘ
characterizing boundedness of composition operators ⓘ characterizing boundedness of singular integral operators ⓘ characterizing boundedness of the Poisson extension operator ⓘ control of non-tangential maximal functions ⓘ control of square functions ⓘ embedding Hardy spaces into L^p spaces with respect to a measure ⓘ interpolation problems in Hardy spaces ⓘ |
| usedIn |
Calderón–Zygmund theory
NERFINISHED
ⓘ
PDE regularity theory ⓘ nonlinear potential theory ⓘ quasiconformal mapping theory ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.