Mathematics - Analysis of PDEs35B4526D10We give a simple proof of Hardy's inequality, based on the logarithmic Caccioppoli estimate for p-superharmonic functions in several variables.doi:10.48550/arXiv.0904.1332Lindqvist, PeterManfredi, JuanMathematics...
he Hardy inequality A probabilistic proof of the Hardy inequalityA probabilistic proof of the Hardy inequalityJensen inequalityScale distributionThis short note provides a fully probabilistic proof to the Hardy inequality.doi:10.1016/j.spl.2015.03.007Walker...
. proof applying hölder’s inequality to \(p_t f(x) = \int _{{\mathbb {r}}^n} p(x,y,t) f(y) dy\) , we find $$\begin{aligned} |p_t f(x)| \le ||f||_p \left( \int _{{\mathbb {r}}^n} p(x,y,t)^{p'} dy\right) ^{\frac{1}{p'}} , \end{aligned}...
In the second section, the non-linear case (a general Hardy-type inequality) is handled with a direct and analytic proof. In the last section, it is illustrated that the basic estimates presented in the first two sections can still be improved considerably. 展开 ...
4 Korn’s Inequality in Other Spaces In this section we note that our proof of Korn’s inequality in a Hardy-Sobolev space yields a similar result in other spaces upon which the Riesz transforms are bounded linear operators. The proof is the same as the one we have given, modulo a chang...
The alternative proofs of Bell's theorem without using Bell's inequality are known as "nonlocality without inequality (NLWI)" proofs. We review one such proof namely the Hardy's proof which due to its simplicity and generality has been considered the best version of Bell's theorem....
(Ω) and all x ∈ Ω. Using this lemma we can easily adopt the proof of [5, Theorem 1] to prove Hardy’s inequality. 3.3. Theorem. Let Ω be an open and bounded subset of R n . Let p: Ω → [1, ∞) be log-H¨older continuous in Ω with 1 < p ...
We give an elementary proof of a family of Hardy–Sobolev-type inequalities with monomial weights. As a corollary, we obtain a weighted trace inequality re... Castro,Hernán - Annali di Matematica Pura ed Applicata (1923 -) 被引量: 1发表: 2017年 Hardy-Sobolev-type inequalities with monomial...
We give a new proof of Hardy's uncertainty principle, up to the end-point case, which is only based on calculus. The method allows us to extend Hardy's uncertainty principle to Schr"odinger equations with non-constant coefficients. We also deduce optimal Gaussian decay bounds for solutions ...
We show that a norm version of Hardy's inequality holds in a variable exponent Sobolev space provided the maximal operator is bounded. Our proof uses recent local versions of the inequality for a fixed exponent. We give an example to show that our assumptions on the exponent are essentially ...