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Hardy-type inequalities related to degenerate elliptic differential operators

Lorenzo D’Ambrosio (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators L p u : = - ∇ L * ( ∇ L u p - 2 ∇ L u ) . If φ is a positive weight such that - L p φ ≥ 0 , then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.

Hardy-type inequality with double singular kernels

Alexander Fabricant, Nikolai Kutev, Tsviatko Rangelov (2013)

Open Mathematics

A Hardy-type inequality with singular kernels at zero and on the boundary ∂Ω is proved. Sharpness of the inequality is obtained for Ω= B 1(0).

Hilbert inequality for vector valued functions

Namita Das, Srinibas Sahoo (2011)

Archivum Mathematicum

In this paper we consider a class of Hankel operators with operator valued symbols on the Hardy space ℋ Ξ 2 ( 𝕋 ) where Ξ is a separable infinite dimensional Hilbert space and showed that these operators are unitarily equivalent to a class of integral operators in L 2 ( 0 , ∞ ) ⊗ Ξ . We then obtained a generalization of Hilbert inequality for vector valued functions. In the continuous case the corresponding integral operator has matrix valued kernels and in the discrete case the sum involves inner product of vectors in the...

Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives

Chun Wang, Tian-Zhou Xu (2015)

Applications of Mathematics

The aim of this paper is to study the stability of fractional differential equations in Hyers-Ulam sense. Namely, if we replace a given fractional differential equation by a fractional differential inequality, we ask when the solutions of the fractional differential inequality are close to the solutions of the strict differential equation. In this paper, we investigate the Hyers-Ulam stability of two types of fractional linear differential equations with Caputo fractional derivatives. We prove that...

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