# hölder s inequality

• ### 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 .

• ### 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.

• ### 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￿

• ### Extensions and demonstrations of Hölder s inequality

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

• ### 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.

• ### 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

• ### 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.

• ### 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

• ### 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.

• ### 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 ¶

• ### 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￿

• ### 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

• ### 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

• ### 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.

• ### 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 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 b_k=ca_k (p-1). (5) If p=q=2 this becomes Cauchy s inequality.

• ### 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.

• ### 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.

• ### 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.

• ### 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

• ### On Subdividing of Hölder s Inequality for Sums

4 S. Abramovich B. Mond J.E. Pečarić Sharpening Hölder s inequality J. Math Anal Appl. 196 (1995) p.1131–1134.

• ### 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

• ### 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

• ### 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￿

• ### 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.

• ### 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

• ### 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.

• ### 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 .