En analyse, l’inégalité de Hölder, ainsi nommée en l'honneur de Otto Hölder, est une inégalité fondamentale relative aux espaces de fonctions Lp, comme les espaces de suites ℓp.

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  • En analyse, l’inégalité de Hölder, ainsi nommée en l'honneur de Otto Hölder, est une inégalité fondamentale relative aux espaces de fonctions Lp, comme les espaces de suites ℓp.
  • In matematica la disuguaglianza di Hölder è un risultato basilare di analisi funzionale. Essa si riferisce agli spazi di funzioni noti come spazi Lp.La disuguaglianza fu provata in una forma leggermente diversa da Leonard James Rogers nel 1888, e riscoperta indipendentemente da Otto Hölder nel 1889, dal quale prende il nome.
  • Em matemática, sobretudo no estudo dos espaços funcionais, a desigualdade de Hölder é uma desigualdade fundamental no estudo dos espaços Lp.
  • In mathematical analysis Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces.Theorem (Hölder's inequality). Let (S, Σ, μ) be a measure space and let p, q ∈ [1, ∞] with 1/p + 1/q = 1. Then, for all measurable real- or complex-valued functions f and g on S,If, in addition, p, q ∈ (1, ∞) and f ∈ Lp(μ) and g ∈ Lq(μ), then Hölder's inequality becomes an equality if and only if |f |p and |g |q are linearly dependent in L1(μ), meaning that there exist real numbers α, β ≥ 0, not both of them zero, such that α |f |p = β |g|q μ-almost everywhere.The numbers p and q above are said to be Hölder conjugates of each other. The special case p = q = 2 gives a form of the Cauchy–Schwarz inequality. Hölder's inequality holds even if ||fg||1 is infinite, the right-hand side also being infinite in that case. Conversely, if f is in Lp(μ) and g is in Lq(μ), then the pointwise product fg is in L1(μ).Hölder's inequality is used to prove the Minkowski inequality, which is the triangle inequality in the space Lp(μ), and also to establish that Lq(μ) is the dual space of Lp(μ) for p ∈ [1, ∞).Hölder's inequality was first found by Rogers (1888), and discovered independently by Hölder (1889).
  • In der mathematischen Analysis gehört die höldersche Ungleichung, benannt nach Otto Hölder, zusammen mit der Minkowski-Ungleichung und der jensenschen Ungleichung zu denfundamentalen Ungleichungen für Lp-Räume.
  • 解析学におけるヘルダーの不等式(- ふとうしき, Hölder's inequality)とは、数列や可測関数のあいだに成り立つもっとも基本的な不等式の一つであり、 測度空間上のLp空間の構造の解析などにしばしば用いられる。オットー・ヘルダーにちなんでこの名前がついている。歴史的には1888年にレオナルド・J・ロジャーズによって、さらにその翌年にヘルダーによって独立に発見された。
  • Hölderova nerovnost je důležitou nerovností v matematické analýze, významnou zejména při zkoumání Lp prostorů.
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  • En analyse, l’inégalité de Hölder, ainsi nommée en l'honneur de Otto Hölder, est une inégalité fondamentale relative aux espaces de fonctions Lp, comme les espaces de suites ℓp.
  • In matematica la disuguaglianza di Hölder è un risultato basilare di analisi funzionale. Essa si riferisce agli spazi di funzioni noti come spazi Lp.La disuguaglianza fu provata in una forma leggermente diversa da Leonard James Rogers nel 1888, e riscoperta indipendentemente da Otto Hölder nel 1889, dal quale prende il nome.
  • Em matemática, sobretudo no estudo dos espaços funcionais, a desigualdade de Hölder é uma desigualdade fundamental no estudo dos espaços Lp.
  • In der mathematischen Analysis gehört die höldersche Ungleichung, benannt nach Otto Hölder, zusammen mit der Minkowski-Ungleichung und der jensenschen Ungleichung zu denfundamentalen Ungleichungen für Lp-Räume.
  • 解析学におけるヘルダーの不等式(- ふとうしき, Hölder's inequality)とは、数列や可測関数のあいだに成り立つもっとも基本的な不等式の一つであり、 測度空間上のLp空間の構造の解析などにしばしば用いられる。オットー・ヘルダーにちなんでこの名前がついている。歴史的には1888年にレオナルド・J・ロジャーズによって、さらにその翌年にヘルダーによって独立に発見された。
  • Hölderova nerovnost je důležitou nerovností v matematické analýze, významnou zejména při zkoumání Lp prostorů.
  • In mathematical analysis Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces.Theorem (Hölder's inequality). Let (S, Σ, μ) be a measure space and let p, q ∈ [1, ∞] with 1/p + 1/q = 1.
rdfs:label
  • Inégalité de Hölder
  • Desigualdad de Hölder
  • Desigualdade de Hölder
  • Desigualtat de Hölder
  • Disuguaglianza di Hölder
  • Hölder Eşitsizliği
  • Hölder's inequality
  • Hölder-Ungleichung
  • Hölder-egyenlőtlenség
  • Hölderova nerovnost
  • Hölderren desberdintza
  • Nierówność Höldera
  • Ongelijkheid van Hölder
  • Неравенство Гёльдера
  • ヘルダーの不等式
  • 횔더 부등식
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