The Meda inequality for rearrangements of the convolution operator on the Heisenberg group Hn is proved. By using the Meda inequality, an O’Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operator MΩ,α and fractional integral operator IΩ,α with rough kernels in the spac...

We give a necessary and sufficient condition on a radially symmetric potential V on a bounded domain Omega of (n) that makes it an admissible candidate for an improved Hardy inequality of the following type. For every element in H(1)(0)(Omega) integral(Omega) |vector differential u|2 dx - ((n - 2)/2)2 integral(Omega) |u|2/|x|2 dx > or = c integral(Omega) V(x)|u|2 dx. A characterization of the b...

Abstract: This paper is considered with the problem of robust absolute stability of neutral type Lur’e systems with mixed time-varying delays. By constructing an new augmented Lyapunov-Krasovskii functional and combining integral inequality with approach to estimate the derivative of the Lyapunov-Krasovskii functional, which estimated some integral terms by Wirtinger’s inequality, a matrix-base...

In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvements based on Wirtinger integral inequality. The potential capability of the proposed WIIs is demonstrated through applications in exponenti...

The delay-dependent decentralized stabilization problem of multi-channel singular time-delay time-invariant systems subject to multiple internal and external incommensurate constant point delays is discussed based on the descriptor integral-inequality approach. The descriptor integral-inequality Lemma is firstly established. Based on the new Lemma and the Lyapunov-Krasovskii functional approach...

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fracti...

In the article, the complete elliptic integrals of the first and second kinds are bounded by using the power series expansions of some functions, the celebrated Wallis inequality, and an integral inequality due to R. P. Agarwal, P. Cerone, S. S. Dragomir and F. Qi. Mathematics subject classification (2010): 26D15, 33C75, 33E05.

In the paper, the authors derive an integral representation, present a double inequality, supply an asymptotic formula, find an inequality, and verify complete monotonicity of a function involving the gamma function and originating from geometric probability for pairs of hyperplanes intersecting with a convex body.

Recently, the author established a general inequality for doubly warped products in arbitrary Riemannian manifolds [14]. In the present paper, we obtain a similar inequality for doubly warped products isometrically immersed in S-space forms. As applications, we derive certain obstructions to the existence of minimal isometric immersions of doubly warped product integral submanifolds in S-space ...

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.