# hölder inequality

• ### Extension of Hölder s inequality (I)

EXTENSION OF HOLDER S INEQUALITY (I) E.G. KWON A continuous form of Holder s inequality is established and used to extend the inequality of Chuan on the arithmetic-geometric mean inequality. 1. Throughout we let X = (X S (i) and Y = (Y T v) be o--finite measure spaces with positive measures fi and v. When we call / defined onXxY measurable it

• ### Hölder type inequalities for matricesEle-Math

2017-10-12 · 15A45 15A42 15A60 47A63 positive semi-definite matrices Hölder inequality trace inequalities weak majorization Oppenheim inequality Created Date 1/1/1998 12 00 00 PM

• ### A matrix reverse Hölder inequalityScienceDirect

2009-11-1 · A matrix reverse Hölder inequality is given. This result is a counterpart to the concavity property of matrix weighted geometric means. It extends a scalar inequality due to Gheorghiu and contains several Kantorovich type inequalities.

• ### Hölder inequalityEncyclopedia of Mathematics

2012-11-29 · In the Hölder inequality the set S may be any set with an additive function μ (e.g. a measure) specified on some algebra of its subsets while the functions a k (s) 1 ≤ k ≤ m are μ -measurable and μ -integrable to degree p k. The generalized Hölder inequality.

• ### probability theoryProving conditional Hölder inequality

2020-8-18 · (This is just putting the conditions for equality into Young s inequality.) In proving the conditional form of Holder s inequality the infimum will be taken over λ a positive F -measurable function.

• ### Hölder s inequality — Wikipedia Republished // WIKI 2

2019-5-30 · 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 was first found by Leonard James Rogers (Rogers (1888)) and discovered independently by Hölder

• ### real analysisHölder inequality and interpolation

2021-1-18 · I found this interpretation of the Hölder inequality. It says that we are trying to find an estimate of ∫fagb with the knowledge of ∫ fp and ∫ gq. For (a b) = (1 1) we need the relationship 1 p 1 q = 1 so that the points (p 0) (1 1) (0 q) lie on the same line. We can know use interpolation to have the Hölder inequality

• ### Otto Hölder (18591937)BiographyMacTutor History

2011-8-29 · Biography Otto Hölder worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series. His father was Otto Hölder (1811-1890) professor of French at the Polytechnikum in Stuttgart the son of Christian

• ### Cauchy-Schwarz Inequality

2020-7-19 · The inequality hold if and only if is proportional to . Proof use lemma Young s inequality 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 . If

• ### A Note on H¨older s Inequality

2009-7-6 · A note on H¨older s inequality 1995 Let x = a b and a ≺ b. (if a b take x = b a). Therefore asbt ≤ as bt. Now replace a and b by 1 −a and 1−b respectively we obtain (1− a)s(1−b)t ≤ s(1− a) t(1− b) =1− sa− tb ≤ 1− asbt. We will now proof Holder s Inequality. 3.2 Holder s Inequality

• ### Inverse Hölder inequalities in one and several dimensions

1973-2-1 · We also prove a multidimensional inverse Hölder inequality for n functions f 1 f n where ∂ 2 f k ∂x i 2 ⩽ 0 i = 1 d k = 1 n. Finally we give an inverse Minkowski inequality for

• ### REMARKS ON THE STABILITY OF HOLDER INEQUALITIES

2016-6-28 · Annales Academia Scientiarum Fennice Series A.I. Mathematica Volumen 10 1985 89-94 Commentationes in honorem Olli Lehto LX annos nato REMARKS ON THE STABILITY OF REYERSE HOLDER INEQUALITIES AND QUASICONFORMAL MAPPINGS B. BOJARSKI In this note we indicate that a refined version of the local Fefferman-Stein inequality for a sharp maximal operator improves

• ### Hölder inequalityEncyclopedia of Mathematics

2012-11-29 · Hölder inequality. The Hölder inequality for sums. Let a s and b s be certain sets of complex numbers s ∈ S where S is a finite or an infinite set of indices. The following inequality of Hölder is valid ( a s b s) and C are independent of s ∈ S. In the limit case when p = 1 q = ∞ Hölder s inequality has the form.

• ### On Hölder s inequality and its applications Octogon

2002-4-1 · The main purpose of the present article is first to give a simple generalizations of Hölder s inequality by using the method of analysis and theory of inequality. Then as applications we improve some new type Pachpatte s inequalities. References 1 . D. S. Mitrinović Analytic inequalities Springer-Verlag New York 1970.

• ### A Note on H¨older s Inequality

2009-7-6 · A note on H¨older s inequality 1995 Let x = a b and a ≺ b. (if a b take x = b a). Therefore asbt ≤ as bt. Now replace a and b by 1 −a and 1−b respectively we obtain (1− a)s(1−b)t ≤ s(1− a) t(1− b) =1− sa− tb ≤ 1− asbt. We will now proof Holder s Inequality. 3.2 Holder s Inequality

• ### Hölder s inequality in nLab

2018-4-5 · Hölder s inequality is closely related to the notion of log-convexity. On the one hand we saw that the inequality follows from the convexity of the exponential function which is the most basic log-convex function of all. On another hand we have the following result which uses Hölder s inequality.

• ### REVERSE HÖLDER MINKOWSKI AND HANNER

2021-4-6 · The Hölder and Minkowski inequalities are well-known inequalities that are fundamental to the study of Lp spaces. The p-Schatten norm jjXjj p= Tr (X X)p=2 1=pis known to also satisfy these inequalities when p 1. Using the technique of majorization 3 ﬁrst established a reverse Minkowski inequality jjA Bjj

• ### REMARKS ON THE STABILITY OF HOLDER INEQUALITIES

2016-6-28 · Annales Academia Scientiarum Fennice Series A.I. Mathematica Volumen 10 1985 89-94 Commentationes in honorem Olli Lehto LX annos nato REMARKS ON THE STABILITY OF REYERSE HOLDER INEQUALITIES AND QUASICONFORMAL MAPPINGS B. BOJARSKI In this note we indicate that a refined version of the local Fefferman-Stein inequality for a sharp maximal operator improves

• ### linear algebraHölder s inequality for matrices

2021-6-5 · There are (at least two) "generalizations" of Hölder inequality to the non-commutative case. One is the so called tracial matrix Hölder inequality langle A B rangle_ HS = mat Tr (A dagger B) le A_p B_q where A_p is the Schatten p -norm and 1/p 1/q=1 . You can find a proof here.

• ### A Proof of Hölder s Inequality Using the Layer Cake

2020-12-8 · A Proof of Hölder s Inequality Using the Layer Cake Representation. Posted by Calvin Wooyoung Chin December 8 2020 December 8 2020 Posted in Notes Tags Analysis Fubini s Theorem Hölder s Inequality Inequality Measure Theory Probability. We prove Hölder s inequality using the so-called layer cake representation and the tensor

• ### Hölder type inequalities for matricesEle-Math

2017-10-12 · 15A45 15A42 15A60 47A63 positive semi-definite matrices Hölder inequality trace inequalities weak majorization Oppenheim inequality Created Date 1/1/1998 12 00 00 PM

• ### Hölder s and Minkowski s Inequalities SpringerLink

FREIMER M. and G. S. MUDHALKAR A class of generalizations of Hölder s inequality Inequalities in Statistics and Probability. IMS Lecture Notes — Monograph Series 5

• ### Hölder s inequality in nLab

2018-4-5 · Hölder s inequality is closely related to the notion of log-convexity. On the one hand we saw that the inequality follows from the convexity of the exponential function which is the most basic log-convex function of all. On another hand we have the following result which uses Hölder s inequality.

• ### Otto Hölder (18591937)BiographyMacTutor History

2011-8-29 · Biography Otto Hölder worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series. His father was Otto Hölder (1811-1890) professor of French at the Polytechnikum in Stuttgart the son of Christian

• ### Inverse Hölder inequalitiesScienceDirect

(4.5) INVERSE HOLDER INEQUALITIES 413 Because of (1.8) inequality (4.1) implies an inverse Holder inequality of the form (1.4) where Cp has the value (1.6). Equality in (1.4) is possible only if there is equality in both (1.4) and the geometric-arithmetic inequality used in (1.8).

• ### Sobolev inequalities and embedding theorems

2008-10-6 · Sobolev inequalities and embedding theorems The simplest Sobolev imbedding th. eorem is the following (trivial) inclusion 4 1

• ### More on Hölder s Inequality and It s Reverse via the

2020-10-18 · Hölder s inequality is one of the greatest inequalities in pure and applied mathematics. As is well known Hölder s inequality plays a very important role in different branches of modern mathematics such as linear algebra classical real and complex analysis probability and statistics qualitative theory

• ### real analysisHölder inequality and interpolation

2021-1-18 · I found this interpretation of the Hölder inequality. It says that we are trying to find an estimate of ∫fagb with the knowledge of ∫ fp and ∫ gq. For (a b) = (1 1) we need the relationship 1 p 1 q = 1 so that the points (p 0) (1 1) (0 q) lie on the same line. We can know use interpolation to have the Hölder inequality

• ### Hölder s Inequalities -- from Wolfram MathWorld

2021-7-19 · Similarly Hölder s inequality for sums states that sum_(k=1) na_kb_k<=(sum_(k=1) na_k p) (1/p)(sum_(k=1) nb_k q) (1/q) (4) with equality when

• ### More on Hölder s Inequality and It s Reverse via the

2020-10-18 · Hölder s inequality is one of the greatest inequalities in pure and applied mathematics. As is well known Hölder s inequality plays a very important role in different branches of modern mathematics such as linear algebra classical real and complex analysis probability and statistics qualitative theory

• ### Extension of Hölder s inequality (I)

EXTENSION OF HOLDER S INEQUALITY (I) E.G. KWON A continuous form of Holder s inequality is established and used to extend the inequality of Chuan on the arithmetic-geometric mean inequality. 1. Throughout we let X = (X S (i) and Y = (Y T v) be o--finite measure spaces with positive measures fi and v. When we call / defined onXxY measurable it

• ### A Note on H¨older s Inequality

2009-7-6 · A note on H¨older s inequality 1995 Let x = a b and a ≺ b. (if a b take x = b a). Therefore asbt ≤ as bt. Now replace a and b by 1 −a and 1−b respectively we obtain (1− a)s(1−b)t ≤ s(1− a) t(1− b) =1− sa− tb ≤ 1− asbt. We will now proof Holder s Inequality. 3.2 Holder s Inequality

• ### A Proof of Hölder s Inequality Using the Layer Cake

2020-12-8 · A Proof of Hölder s Inequality Using the Layer Cake Representation. Posted by Calvin Wooyoung Chin December 8 2020 December 8 2020 Posted in Notes Tags Analysis Fubini s Theorem Hölder s Inequality Inequality Measure Theory Probability. We prove Hölder s inequality using the so-called layer cake representation and the tensor

• ### Hölder inequalityin m

Hölder s inequality is a basic inequality in analysis used to prove that if the sum of positive numbers p q equals their product then the Banach spaces L p L q are Banach duals of one another. Statements 0. The rst thing to note is Young s inequality is a far-reaching generalization of Cauchy s inequality.

• ### probability theoryProving conditional Hölder inequality

2020-8-18 · Alternatively the standard Hölder s inequality gives us mathbb Eleft XYright

• ### probability theoryProving conditional Hölder inequality

2020-8-18 · Alternatively the standard Hölder s inequality gives us mathbb Eleft XYright

• ### (Hölder s Inequality)

2020-10-23 · 2 . (1)Jensen s Inequality. Jensen s Inequality. . . . .

• ### A generalized Hölder-type inequalities for measurable

2020-8-8 · We prove a generalized Hölder-type inequality for measurable operators associated with a semi-finite von Neumann algebra which is a generalization of the result shown by Bekjan (Positivity 21 113–126 2017). This also provides a generalization of the unitarily invariant norm inequalities for matrix due to Bhatia–Kittaneh Horn–Mathisa Horn–Zhan and Zou under a cohyponormal condition.

• ### A matrix reverse Hölder inequalityScienceDirect

2009-11-1 · A matrix reverse Hölder inequality is given. This result is a counterpart to the concavity property of matrix weighted geometric means. It extends a scalar inequality due to Gheorghiu and contains several Kantorovich type inequalities.

• ### Hölder type inequalities for matricesEle-Math

2017-10-12 · 15A45 15A42 15A60 47A63 positive semi-definite matrices Hölder inequality trace inequalities weak majorization Oppenheim inequality Created Date 1/1/1998 12 00 00 PM