# hölder s inequality

• ### Generalized Hölder s inequality for g-integral IEEE

2016-8-31 · Generalized Hölder s inequality for g-integral Abstract One extension of Hölder inequality in the frame of pseudo-analysis is given. The extension of Hölder inequality is presented for the case of g-semirings and some illustrative examples are given. Published

• ### 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

• ### Young s Minkowski s and H older s inequalities

2011-9-16 · The rst thing to note is Young s inequality is a far-reaching generalization of Cauchy s inequality. In particular if p = 2 then 1 p = p 1 p = 1 2 and we have Cauchy s inequality ab 1 2 a2 1 2 b2 (4) Normally to use Young s inequality one chooses a speci c p and a and b are free-oating quantities. For instance if p = 5 we get

• ### Hölder s identity — Princeton University

We clarify that Hölder s inequality can be stated more generally than is often realized. This is an immediate consequence of an analogous information-theoretic identity which we call Hölder s identity. We also explain Andrew R. Barron s original use of the identity.

• ### Young s Minkowski s and H older s inequalities

2011-9-16 · The rst thing to note is Young s inequality is a far-reaching generalization of Cauchy s inequality. In particular if p = 2 then 1 p = p 1 p = 1 2 and we have Cauchy s inequality ab 1 2 a2 1 2 b2 (4) Normally to use Young s inequality one chooses a speci c p and a and b are free-oating quantities. For instance if p = 5 we get

• ### Sobolev inequalities and embedding theorems

2008-10-6 · s the so­called critical Sobolev s exponent and ã depends only on L and J. The crucial step is to prove the Sobolev inequality for The first case L Ú. Notice that it suffices only to prove (2) for test functions that is Ð 4 ¶ 7 . We extend any given R Ð 4 ¶

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• ### 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.

• ### 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

• ### 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 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.

• ### 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.

• ### Ele-MathKeyword page Hölder inequality

Articles containing keyword "Hölder inequality" MIA-01-01 » Hölder type inequalities for matrices (01/1998) MIA-01-05 » Why Hölder s inequality should be called Rogers inequality (01/1998) MIA-01-37 » Some new Opial-type inequalities (07/1998) MIA-02-02 » A note on some classes of Fourier coefficients (01/1999) MIA-03-37 » Generalization theorem on convergence and integrability for

• ### real analysisProving Hölder s InequalityMathematics

2021-6-10 · In the vast majority of books dealing with Real Analysis Hölder s inequality is proven by the use of Young s inequality for the case in which p q > 1 and they usually have as an exercise the question whether this inequality is valid for p = 1 which means that q = ∞ . Well if f ∈ L1 and g ∈ L∞ then ‖f‖1 = ∫b a f(x) dx

• ### 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.

• ### Extensions and demonstrations of Hölder s inequality

2019-4-8 · YanandGao JournalofInequalitiesandApplications20192019 97 Page2of12 Yang s 13 14 insightsintoinequalitieshavefurtherledtoseveralinferences.Qi s 15 16

• ### Improving Hölder s inequality

2021-6-19 · Improving Hölder s inequality Satyanad Kichenassamy To cite this version Satyanad Kichenassamy. Improving Hölder s inequality. Houston Journal of Mathematics 2010 35 (1) pp.303-312. ￿hal-00826949￿

• ### The Improvement of Hölder s Inequality with -Conjugate

Abstract. This paper investigates Hölder s inequality under the condition of -conjugate exponents in the sense that . Successively we have under -conjugate exponents relative to the -norm investigated generalized Hölder s inequality the interpolation of Hölder s inequality and generalized -order Hölder s inequality which is an expansion of the known Hölder s inequality.

• ### Hölder s Inequality and Related Inequalities in

Hölder s Inequality and Related Inequalities in Probability 10.4018/jalr.2011010106 In this paper the author examines Holder s inequality and related inequalities in probability. The paper establishes new inequalities in probability that

• ### Cauchy-Schwarz Inequality

2020-7-19 · Young s inequality can be used to prove Hölder s inequality. It is also widely used to estimate the norm of nonlinear terms in PDE theory since it allows one to estimate a product of two terms by a sum of the same terms raised to a power and scaled .

• ### 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.

• ### Improving Hölder s inequality

2021-6-19 · Improving Hölder s inequality Satyanad Kichenassamy To cite this version Satyanad Kichenassamy. Improving Hölder s inequality. Houston Journal of Mathematics 2010 35 (1) pp.303-312. ￿hal-00826949￿

• ### A Class of Generalizations of Hölder s Inequality

der s inequality using arguments of convex analysis. In Section 2 we formulate an optimi-zation problem and obtain (1.4) as its solution using a constructive method namely the Kuhn-Tucker theory. A Class of Generalizations of Hölder 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

• ### Generalizations of Hölder s and some related inequalities

2011-1-1 · Then it is well known that the following Hölder inequality holds (see) (1.1) Similarly the integral form of the Hölder inequality is (1.2) where and. If and then inequalities (1.1) (1.2) reduce to the famous Cauchy inequalities (see) of the discrete version and the continuous version respectively.

• ### Sharpening Hölder s inequalityKTH

2018-2-5 · Sharpening Hölder s inequality Author H. Hedenmalm (joint work with D. Stolyarov V. Vasyunin P. Zatitskiy) Created Date 2/5/2018 1 38 43 PM

• ### Cauchy-Schwarz Inequality

2020-7-19 · 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.

• ### real analysisProving Hölder s InequalityMathematics

2021-6-10 · In the vast majority of books dealing with Real Analysis Hölder s inequality is proven by the use of Young s inequality for the case in which p q > 1 and they usually have as an exercise the question whether this inequality is valid for p = 1 which means that q = ∞ . Well if f ∈ L1 and g ∈ L∞ then ‖f‖1 = ∫b a f(x) dx

• ### Hölder s inequalityScienceDirect

2003-8-1 · Then it is well known that the following Hder s inequality holds 1 m n fi(m 1/Pi dij < a (1) i=1 j=1 j=1i=1 If we define a function h (-oo oo) -a (0 oo) as 1_t 1/Pk n m n h(t) = 11 1 rJ aij (ask) (2) k=1 i=1 j=1 then it is easy to see h E C and (1) becomes m n n m 1/Pi h(0) _ E I I sij <_ E Qp3 = j( (1) (3) i=1 j=1 j_1 i=1 From (2) and (3) it is natural to consider the function h(t) more deeply.

• ### Hölder s identity — Princeton University

We clarify that Hölder s inequality can be stated more generally than is often realized. This is an immediate consequence of an analogous information-theoretic identity which we call Hölder s identity. We also explain Andrew R. Barron s original use of the identity.

• ### Symmetry Free Full-Text More on Hölder s Inequality

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 of differential equations and their applications.

• ### Extensions and demonstrations of Hölder s inequality

2019-4-8 · YanandGao JournalofInequalitiesandApplications20192019 97 Page2of12 Yang s 13 14 insightsintoinequalitieshavefurtherledtoseveralinferences.Qi s 15 16

• ### Bounding the Partition Function using Hölder s Inequality

2019-1-10 · Bounding the Partition Function using H older s Inequality Qiang Liu qliu1 uci.edu Alexander Ihler ihler ics.uci.edu Department of Computer Science University of California Irvine CA 92697 USA Abstract We describe an algorithm for approximate in-ference in graphical models based on H older s inequality that provides upper and lower

• ### Young s Minkowski s and H older s inequalities

2011-9-16 · The rst thing to note is Young s inequality is a far-reaching generalization of Cauchy s inequality. In particular if p = 2 then 1 p = p 1 p = 1 2 and we have Cauchy s inequality ab 1 2 a2 1 2 b2 (4) Normally to use Young s inequality one chooses a speci c p and a and b are free-oating quantities. For instance if p = 5 we get

• ### Sharpening Hölder s inequalityKTH

2018-2-5 · Sharpening Hölder s inequality Author H. Hedenmalm (joint work with D. Stolyarov V. Vasyunin P. Zatitskiy) Created Date 2/5/2018 1 38 43 PM

• ### Bounding the Partition Function using Hölder s Inequality

2019-1-10 · Bounding the Partition Function using H older s Inequality Qiang Liu qliu1 uci.edu Alexander Ihler ihler ics.uci.edu Department of Computer Science University of California Irvine CA 92697 USA Abstract We describe an algorithm for approximate in-ference in graphical models based on H older s inequality that provides upper and lower

• ### Hölder s identity — Princeton University

We clarify that Hölder s inequality can be stated more generally than is often realized. This is an immediate consequence of an analogous information-theoretic identity which we call Hölder s identity. We also explain Andrew R. Barron s original use of the identity.

• ### 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

• ### 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

• ### functional analysisHölder s inequality with three

2021-6-12 · Hölder s inequality with three functions. Let p q r ∈ (1 ∞) with 1 / p 1 / q 1 / r = 1. Prove that for every functions f ∈ Lp(R) g ∈ Lq(R) and h ∈ Lr(R) ∫R fgh ≤ ‖f‖p ⋅ ‖g‖q ⋅ ‖h‖r.

• ### Hölder s Inequality Brilliant Math Science Wiki

Hölder s inequality is often used to deal with square (or higher-power) roots of expressions in inequalities since those can be eliminated through successive multiplication. Here is an example Let a b c a b c a b c be positive reals satisfying a b c = 3 a b c=3 a b c = 3 .