Hardy's inequality was first published and proved (at least the discrete version with a worse constant) in 1920 in a note by Hardy. The original formulation was in an integral form slightly different from the above. See more Hardy's inequality is an inequality in mathematics, named after G. H. Hardy. It states that if $${\displaystyle a_{1},a_{2},a_{3},\dots }$$ is a sequence of non-negative real numbers, then for every real number p > 1 … See more Integral version A change of variables gives Discrete version: from the continuous version Assuming the right-hand side to be finite, we must have $${\displaystyle a_{n}\to 0}$$ See more • Carleman's inequality See more • "Hardy inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994] See more The general weighted one dimensional version reads as follows: • If $${\displaystyle \alpha +{\tfrac {1}{p}}<1}$$, … See more In the multidimensional case, Hardy's inequality can be extended to $${\displaystyle L^{p}}$$-spaces, taking the form where $${\displaystyle f\in C_{0}^{\infty }(R^{n})}$$, … See more 1. ^ Hardy, G. H. (1920). "Note on a theorem of Hilbert". Mathematische Zeitschrift. 6 (3–4): 314–317. doi:10.1007/BF01199965. S2CID 122571449. 2. ^ Hardy, G. H.; Littlewood, J.E.; Pólya, G. (1952). Inequalities (Second ed.). Cambridge, UK. See more WebJun 5, 2024 · The inequalities are valid for all functions for which the right-hand sides are finite, except when $ f $ vanishes almost-everywhere on $ ( 0, + \infty ) $. (In this case …
Weighted inequalities of Hardy type - 百度学术
WebHardy-type inequalities. Bohumír Opic, Alois Kufner. 31 Dec 1989 -. TL;DR: In this article, the one-dimensional Hardy inequality is defined as an imbedding of a weighted … WebDec 2, 2024 · A complete Riemannian manifold equipped with some potential function and an invariant conformal measure is referred to as a complete smooth metric measure space. This paper generalizes some integral inequalities of the Hardy type to the setting of a complete non-compact smooth metric measure space without any geometric constraint … blackberry\u0027s 73
Hardy type inequalities in generalized grand Lebesgue spaces
WebAug 18, 2024 · In this paper, we study some ( p, q) -Hardy type inequalities for ( p, q) -integrable functions. Moreover, we also study ( p, q) -H?lder integral inequality and ( p, q) -Minkowski integral inequality for two variables. By taking p = 1 and q → 1, our results reduce to classical results on Hardy type inequalities, H?lder integral inequality and ... WebThe classical Hardy inequality was first proved by G. Hardy [142]. The various extensions of this inequality as well the proof of Theorem 2.8 can be found in [362, 108]. For other … WebAbstract. In this paper, we use Taylor’s formula to prove new Hardy-type inequalities involving convex functions. We give new results that involve the Hardy–Hilbert inequality, … galaxy movie theater austin texas