Carleson (other)
Carleson may refer to: Mathematics * Carleson measure, a mathematical method applied to dimensional space * Carleson's inequality, a generalisation of Carleman's inequality * Carleson–Jacobs theorem, a function applied to the unit of a circle People * Carleson, a Swedish surname See also *Charleson Charleson is a given name and a surname. Notable people with the name include: Surname * Bill Charleson (1929–1983), Australian rules footballer *Ian Charleson (1949–1990), Scottish actor *Leslie Charleson (born 1945), American actress *Mary Ch ...

Carleson Measure
In mathematics, a Carleson measure is a type of measure on subsets of ''n''-dimensional Euclidean space R''n''. Roughly speaking, a Carleson measure on a domain Ω is a measure that does not vanish at the boundary of Ω when compared to the surface measure on the boundary of Ω. Carleson measures have many applications in harmonic analysis and the theory of partial differential equations, for instance in the solution of Dirichlet problems with "rough" boundary. The Carleson condition is closely related to the boundedness of the Poisson operator. Carleson measures are named after the Swedish mathematician Lennart Carleson. Definition Let ''n'' ∈ N and let Ω ⊂ R''n'' be an open (and hence measurable) set with non-empty boundary ∂Ω. Let ''μ'' be a Borel measure on Ω, and let ''σ'' denote the surface measure on ∂Ω. The measure ''μ'' is said to be a Carleson measure if there exists a constant ''C'' > 0 such that, for every point ''p ...
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Carleman's Inequality
Carleman's inequality is an inequality in mathematics, named after Torsten Carleman, who proved it in 1923 and used it to prove the Denjoy–Carleman theorem on quasi-analytic classes. Statement Let a_1,a_2,a_3,\dots be a sequence of non-negative real numbers, then : \sum_^\infty \left(a_1 a_2 \cdots a_n\right)^ \le \mathrm \sum_^\infty a_n. The constant \mathrm (euler number) in the inequality is optimal, that is, the inequality does not always hold if \mathrm is replaced by a smaller number. The inequality is strict (it holds with "<" instead of "≤") if some element in the sequence is non-zero. Integral version Carleman's inequality has an integral version, which states that : \int_0^\infty \exp\left\ \,\mathrmx \leq \mathrm \int_0^\infty f(x) \,\mathrmx for any ''f'' ≥ 0. Carleson's inequality A generalisation, due to Lennart Carleson, states the following: for any convex function ''g'' with ''g''(0) = 0, and for any -1  1, r ...
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Carleson–Jacobs Theorem
In mathematics, the Carleson–Jacobs theorem, introduced by , describes the best approximation to a continuous function In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value ... on the unit circle by a function in a Hardy space. Notes References * * Theorems in complex analysis Hardy spaces {{Mathanalysis-stub ...
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Carleson
Carleson is a Swedish patronymic surname. Notable people with the surname include: *C. N. Carleson (1865–1929), Swedish politician *Edvard Carleson (1820–1884), Swedish politician * Lennart Carleson (born 1928), Swedish mathematician *Per Carleson (1917–2004), Swedish fencer *Robert B. Carleson (1931–2006), American presidential advisor See also *Carlson (other) Carlson may refer to: * Carlson (name), people with the given name or surname * Carlson Companies, American conglomerate ** CWT, subsidiary ** Radisson Hotel Group, former subsidiary formerly known as Carlson Rezidor * Carlson Inlet, Antarctica * ...