A note on a class of Hardy-Rellich type inequalities

Di, Yanmei; Jiang, Liyu; Shen, Shoufeng; Jin, Yongyang

doi:10.1186/1029-242x-2013-84

Cited by 9 publications

(9 citation statements)

References 8 publications

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“…From these expressions of h, we obtain the explicit function f in (3.8). By approximating this function f on R N and the constant function on R N 2 × • • • × R Nr by compactly supported function, we obtain the sharpness of (1.15) and (1.16) (see [9] for a special case p = q = r in R n ).…”

Section: Proof Of Theorem 11mentioning

confidence: 95%

Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups

Nguyen¹

2018

Ann. Acad. Sci. Fenn. Math.

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In this paper, we prove a family of sharp Caffarelli-Kohn-Nirenberg inequalities on stratified Lie groups. Our result sharpens the inequalities obtained recently by Ruzhansky, Suragan and Yessirkegenov [22], and extend the classical Caffarelli-Kohn-Nirenberg inequalities to a new class of exponents (negative or smaller than 1) which we believe to be new in literature. Finally, we generalize our result to the more general setting of homogeneous groups with any homogeneous quasi-norm.

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Section: Proof Of Theorem 11mentioning

confidence: 95%

Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups

Nguyen¹

2018

Ann. Acad. Sci. Fenn. Math.

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“…. + x 2 n , implies the L p -Caffarelli-Kohn-Nirenberg type inequality (see [DJSJ13] and [Cos08]) for G ≡ R n with the sharp constant:…”

Section: P -Caffarelli-kohn-nirenberg Type Inequalities and Consequmentioning

confidence: 99%

Lp-Caffarelli–Kohn–Nirenberg type inequalities on homogeneous groups

Ozawa

Ruzhansky

Сураган

2018

The Quarterly Journal of Mathematics

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We prove L p -Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already in the Abelian cases of isotropic or anisotropic R n our results provide new conclusions in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.2010 Mathematics Subject Classification. 22E30, 43A80.

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“…, ∂ xn ), so (3.1) implies the L p -Caffarelli-Kohn-Nirenberg type inequality (see e.g. [10] and [18]) for G ≡ R n with the sharp constant:…”

Section: Horizontal L P -Caffarelli-kohn-nirenberg Type Inequalities ...mentioning

confidence: 99%

On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups

Ruzhansky

Сураган

2017

Journal of Differential Equations

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In this paper, we present a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in special cases. Moreover, a new simple proof of the Badiale-Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided. We also show a family of Poincaré inequalities as well as inequalities involving the weighted and unweighted p-sub-Laplacians.2010 Mathematics Subject Classification. 22E30, 43A80.

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A note on a class of Hardy-Rellich type inequalities

Abstract: In this note we provide simple and short proofs for a class of Hardy-Rellich type inequalities with the best constant, which extends some recent results. MSC: 26D15; 35A23

Cited by 9 publications

References 8 publications

Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups

Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups

Lp-Caffarelli–Kohn–Nirenberg type inequalities on homogeneous groups

On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups

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