### 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 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

### 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

### 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

### 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

### 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.

### 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

### 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

### 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 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.

### 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

### 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

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

### 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

### 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

### 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).

### 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

### 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.

### 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

### 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 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.

### 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

### 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 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

### 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