Hilbert's inequalities and their reverses

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August undefined, 2024

WebNov 29, 2024 · Hilbert's inequalities and their reverses Authors: Mario Krnić University of Zagreb Josip Pečarić University of Zagreb Request full-text Abstract In this paper, we … WebInequalities; Hilbert's inequality; Holder's inequality; reverse inequalities; equivalent inequalities Sažetak In this paper, we make some further generalizations of well known …

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WebWe obtain a generalized discrete Hilbert and Hardy-Hilbert inequality with non-conjugate parameters by means of an Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our findings with existing results. We improve some earlier results and apply the results to some special homogeneous functions. WebSome equivalent conditions of a reverse Hilbert-type integral inequality with the particular homogeneous kernel are deduced. We also consider some particular cases. Mathematics … shards of the crown

Hilbert problems - Encyclopedia of Mathematics

WebSep 1, 2013 · Hilbert’s inequalities and their reverses. Publicationes Mathematicae Debrecen (2005) B.C. Yang et al. On a best value of Hardy–Hilbert’s inequality. Advances in Mathematics (1997) M.Z. Gao et al. On the extended Hilbert’s inequality. Proceedings of the American Mathematical Society WebJul 3, 2012 · By using the way of weight functions and the technique of real analysis, a half-discrete Hilbert-type inequality with a general nonhomogeneous kernel and two interval variables, as well as a best constant factor is given. The equivalent forms, the operator expressions, the reverses and some particular examples are considered. WebThe equivalent forms, the reverses and some Hardy-type inequalities are obtained. Furthermore, we consider the operator expressions with the norm, some particular inequalities and a large number of examples. The theory of multidimensional Hilbert-type inequalities and the operator expressions are built in this book. pooley removals suffolk

Hilbert

WebOct 1, 2015 · The Hilbert-type inequalities are a more wide class of analysis inequalities which are with the bilinear kernels, including Hardy-Hilbert's inequality as the particular case. These... WebIn this paper, with the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalized a number of Hilbert-type inequalities to a general time scale. Besides that, in order to obtain some new inequalities as special cases, we also extended our inequalities to discrete and continuous calculus. shards of wuuthradhttp://files.ele-math.com/abstracts/jmi-08-18-abs.pdf pooley phonograph

"Web1 Answer. This works fine provided that you know all the sums are finite. An easy way to see it is to let a ( n) = f, f n , b ( n) = f, f n − g n . Then your inequalities read. where ⋅ is the ℓ 2 norm, and this is a simple consequence of the triangle inequality for the ℓ 2 norm. . " - Hilbert's inequalities and their reverses

Hilbert's inequalities and their reverses

WebNov 4, 2024 · A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function. Appl. Math. Comput. 225, 263–277 (2013) MathSciNet MATH Google Scholar … WebMar 18, 2024 · Hilbert's fourth problem. The problem of the straight line as the shortest distance between two points. This problem asks for the construction of all metrics in …

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WebApr 12, 2024 · Hilbert-Schmidt 框架序列的斜 ... 摘要： The classical inequalities of Clarkson for the Lebesgue space and their non-commutative analogues for the Schatten trace ideals play an important role in analysis, operator theory and mathematical physics. In this talk, we introduce the development of Clarkson Inequalities and obtain extensions ...

WebThe use of algorithms as a functional strategy puts the institutional decision-making paradigms to test and their endurance in the actual functioning of the institutions. ... 2024, 265 pp. 12. Davide Beraldo, Cathy O’Neil, Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy, New York, Broadway Books, 2016 ... WebApr 27, 2024 · In 1934, a half-discrete Hilbert-type inequality was given as follows (cf. [ 1 ], Theorem 351): If K (t) ( t > 0) is a decreasing function, p > 1, \frac {1} {p} + \frac {1} {q} = 1, 0 < \phi (s) = \int _ {0}^ {\infty } K (t)t^ {s - 1}\,dt < \infty , a_ {n} \ge 0, 0 < \sum_ {n = 1}^ {\infty } a_ {n}^ {p} < \infty , then we have

WebHilbert-type inequalities including Hilbert’s inequalities (built-in 1908), Hardy-Hilbert-type inequalities (built-in 1934), and Yang-Hilbert-type inequalities (built-in 1998) played an important role in analysis and their applications, which are mainly divided into three classes of integral, discrete and half-discrete. In recent twenty years, there are many advances in … WebDec 15, 2024 · This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s …

WebDec 1, 2013 · Using the method of weight functions and techniques of discrete and integral Hilbert-type inequalities with some additional conditions on the kernel, the following half-discrete Hilbert-type inequality with a general homogeneous kernel of degree -λ ∈ R and the best constant factor k λ 1 is obtained ∫ 0 ∞ f (x) ∑ n = 1 ∞ k λ (x, n ...

WebON AN EQUIVALENT PROPERTY OF A REVERSE HILBERT–TYPE INTEGRAL INEQUALITY RELATED TO THE EXTENDED HURWITZ–ZETA FUNCTION MICHAELTH.RASSIAS ANDBICHENGYANG ... [12] M. KRNIC´,J.E.PECARIˇ C´, Hilbert’s inequalities and their reverses, Publ. Math. Debrecen, 2005, 67(3-4), 315–331. pooley ranchWebMar 12, 2024 · Similar work about Hilbert-type integral inequalities is in [22–26]. In this paper, following the way of [2, 21], by the use of the weight coefficients, the idea of … pooley tomsWebOct 1, 2005 · Hilbert's inequalities and their reverses. In this paper, we make some further generalizations of well known Hilbert's inequality and its equivalent form in both integral … pooleys ppl books pdfWeb1: Recent Developments of Hilbert-Type Inequalities with Applications. 2: Improvements of the Euler-Maclaurin Summation Formula and Applications. 3: A Half-Discrete Hilbert-Type Inequality with a General Homogeneous Kernel. 4: A Half-Discrete Hilbert-Type Inequality with a Non-Homogeneous Kernel. pooley weighbridgeWeb一个逆向Hilbert型不等式的最佳推广[J].武汉大学学报:理学版,2008,54(3):275-278. WANG Aizhen, YANG Bicheng. A best generalization of reverse Hilbert-type inequality[J]. J Wuhan Univ: Natural Science Edition, 2008,54(3):275-278. Keywords： Hilbert-type intergral inequality; weight function; equivalent form; Hölder’s inequality shards of wisdomWebJan 1, 2008 · An extension of the Hilbert-type inequality and its reverse DOI: 10.7153/jmi-02-14 Authors: Bicheng Yang Guangdong University of Education Abstract By introducing some parameters and the weight... shards of zhaitan gw2WebMar 24, 2024 · Hilbert's Inequality. Given a positive sequence , (1) where the s are real and "square summable." Another inequality known as Hilbert's applies to nonnegative sequences and , (2) unless all or all are 0. If and are nonnegative integrable functions, then the … pooley wheels