NettetAbstract. In this paper, we shall prove that for n>1, the n-dimensional Jensen inequality holds for the g-expectation if and only if g is independent of y and linear with respect to z, in other ... Nettet1977] HOLDER INEQUALITY 381 If fxf2 € Lr9 then (3-2) IIMIp = (j [(/1/2)/ï 1]p}1'P ^HA/ 2 r /2 t\ llfiHp IIM^I/i/A This generalized reverse Holder inequality (3.2) holds also, trivially, if /i^éL,, so it holds in general. We now transliterate inverses of the generalized Holder inequality into inverses of the generalized reverse Holder ...
Hölder
NettetThe Hölder inequality is a generalization of this. Applications [ edit] Analysis [ edit] In any inner product space, the triangle inequality is a consequence of the Cauchy–Schwarz inequality, as is now shown: … Hölder's inequality is used to prove the Minkowski inequality, which is the triangle inequality in the space L p (μ), and also to establish that L q (μ) is the dual space of L p (μ) for p ∈ [1, ∞). Hölder's inequality (in a slightly different form) was first found by Leonard James Rogers . Se mer In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of L spaces. The numbers p and q … Se mer Statement Assume that 1 ≤ p < ∞ and let q denote the Hölder conjugate. Then for every f ∈ L (μ), where max indicates that there actually is a g maximizing the … Se mer Statement Assume that r ∈ (0, ∞] and p1, ..., pn ∈ (0, ∞] such that $${\displaystyle \sum _{k=1}^{n}{\frac {1}{p_{k}}}={\frac {1}{r}}}$$ where 1/∞ is interpreted as 0 in this equation. Then for all … Se mer It was observed by Aczél and Beckenbach that Hölder's inequality can be put in a more symmetric form, at the price of introducing an extra vector (or function): Let Se mer Conventions The brief statement of Hölder's inequality uses some conventions. • In the definition of Hölder conjugates, 1/∞ means zero. Se mer For the following cases assume that p and q are in the open interval (1,∞) with 1/p + 1/q = 1. Counting measure For the n-dimensional Euclidean space, when the set S is {1, ..., n} with the counting measure, … Se mer Two functions Assume that p ∈ (1, ∞) and that the measure space (S, Σ, μ) satisfies μ(S) > 0. Then for all measurable real- or complex-valued functions f and g on S such that g(s) ≠ 0 for μ-almost all s ∈ S, Se mer take off shoes in house
Hölder inequality - Encyclopedia of Mathematics
NettetIn Section 2 we establish a continuous form of Holder's inequality. In Section 3 we give an application of the inequality by generalising a result of Chuan [2] on the arithmetic-geometric mean inequality. In Section 4, we give further extensions of the result of Section 3. 2. If 0 Sj x ^ 1, then Holder's inequality says that (2.1) JYMy)'f2(y) 1 ... Nettet2. jul. 2024 · In the Holder inequality, we have ∑ x i y i ≤ ( ∑ x i p) 1 p ( ∑ y i q) 1 q, where 1 p + 1 q = 1, p, q > 1. In Cauchy inequality (i.e., p = q = 2 ), I know that the equality holds if and only if x and y are linearly dependent. I am wondering when the equality holds in the Holder inequality. real-analysis functional-analysis inequality Nettet13. mar. 2024 · Hölder's inequality can be proved using Young's inequality, for which a beautiful intuition is given here. In my perspective, even though this gives intuition to a … twitch black screen reddit