Results 1 to 10 of about 1,472 (177)

The refinement and generalization of Hardy’s inequality in Sobolev space [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend the integral estimation function from u|x| $
Xiaomin Xue, Fushan Li
doaj   +2 more sources

On Carleson’s inequality [PDF]

Journal of Inequalities and Applications, 2018
We present a new proof of Hardy’s inequality by giving an Lp $L^{p}$ version of Carleson’s inequality.
Ern Gun Kwon
doaj   +2 more sources

Hardy-type inequalities in fractional h-discrete calculus [PDF]

Journal of Inequalities and Applications, 2018
The first power weighted version of Hardy’s inequality can be rewritten as ∫0∞(xα−1∫0x1tαf(t)dt)pdx≤[pp−α−1]p∫0∞fp(x)dx,f≥0,p≥1 ...
Lars-Erik Persson, Ryskul Oinarov, Serikbol Shaimardan   +2 more
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New Strengthened Carleman's Inequality and Hardy's Inequality [PDF]

Journal of Inequalities and Applications, 2007
In this note, new upper bounds for Carleman's inequality and Hardy's inequality are established.
Ling Zhu, Haiping Liu
doaj   +4 more sources

Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group

Bulletin of Mathematical Sciences, 2016
We prove geometric $$L^p$$ L p versions of Hardy’s inequality for the sub-elliptic Laplacian on convex domains $$\Omega $$ Ω in the Heisenberg group $$\mathbb {H}^n$$ H n , where convex is meant in the Euclidean sense.
Simon Larson
doaj   +4 more sources

Generalizations of Hardy Type Inequalities by Abel–Gontscharoff’s Interpolating Polynomial

Mathematics, 2021
In this paper, we extend Hardy’s type inequalities to convex functions of higher order. Upper bounds for the generalized Hardy’s inequality are given with some applications.
Kristina Krulić Himmelreich, Josip Pečarić, Dora Pokaz, Marjan Praljak   +3 more
doaj   +1 more source

Finsler Hardy–Kato's inequality [PDF]

Journal of Mathematical Analysis and Applications, 2019
We prove an improved version of the trace-Hardy inequality, so-called Kato's inequality, on the half-space in Finsler context. The resulting inequality extends the former one obtained by \cite{AFV} in Euclidean context. Also we discuss the validity of the same type of inequalities on open cones.
Alvino, A., Ferone, A., Mercaldo, A., Takahashi, F., Volpicelli, R.   +4 more
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Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions

Axioms, 2023
In this paper we extend general Hardy’s inequality by appropriately combining Montgomery’s identity and Green functions. Related Grüss and Ostrowski-type inequalities are also derived.
Kristina Krulić Himmelreich, Josip Pečarić, Dora Pokaz, Marjan Praljak   +3 more
doaj   +1 more source

Hardy inequalities [PDF]

Proceedings of the American Mathematical Society, 1990
Here the following Hardy inequalities are studied \[ ∑ k = 0 m − 1 ∫ | ∇
openaire   +2 more sources

Ground states of coupled critical Choquard equations with weighted potentials [PDF]

Opuscula Mathematica, 2022
In this paper, we are concerned with the following coupled Choquard type system with weighted potentials \[\begin{cases} -\Delta u+V_{1}(x)u=\mu_{1}(I_{\alpha}\!\ast\![Q(x)|u|^{\frac{N+\alpha}{N}}])Q(x)|u|^{\frac{\alpha}{N}-1}u+\beta(I_{\alpha}\!\ast\![Q(
Gaili Zhu, Chunping Duan, Jianjun Zhang, Huixing Zhang   +3 more
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