By introducing multi-parameters, applying the weight coefficients and Hermite-Hadamard's inequality, we give a reverse of the extended Mulholland inequality in the whole plane with the best possible constant factor. The equivalent forms and a few particular cases are also considered.

Let ( X , ρ μ ) $({\mathcal {X}},\rho ,\mu )$ be a space of homogeneous type in the sense Coifman and Weiss, let Y $Y({\mathcal {X}})$ ball quasi-Banach function on ${\mathcal {X}}$ which supports both Fefferman–Stein vector-valued maximal inequality boundedness powered Hardy–Littlewood operator its associate space. The authors first introduce Hardy H ∗ $H_{Y}^*({\mathcal associated with via gr...

By using the Euler-Maclaurin’s summation formula and the weight coefficient, a pair of new inequalities is given, which is a decomposition of Hilbert’s inequality. The equivalent forms and the extended inequalities with a pair of conjugate exponents are built.

There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequ...

This manuscript develops the study of reverse Hilbert-type inequalities by applying Hölder on T. We generalize inequality with power two replacing a new β,β>1. The main results are proved using Specht’s ratio, chain rule and Jensen’s inequality. Our (when T=N) essentially new. Symmetrical properties play an essential role in determining correct methods to solve inequalities.

We give a systematic study on the Hardy spaces of functions with values in the non-commutative L-spaces associated with a semifinite von Neumann algebra M. This is motivated by the works on matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), and on the other hand, by the recent development on the non-commutative martingale inequalities. Our non-com...

Inspired by the forward and the reverse channels from the image-size characterization 1 problem in network information theory, we introduce a functional inequality which unifies 2 both the Brascamp-Lieb inequality and Barthe’s inequality, which is a reverse form of the 3 Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using 4 the Legendre-Fenchel dualit...

In 2012, W. T. Sulaiman presented new kinds of Hardy’s integral inequalities. In this paper, we derive some new extensions of the famous Hardy’s integral inequality. The results present direct generalization of the original Hardy inequality. In addition, the corresponding reverse relation is also obtained.

We prove an inequality on positive real numbers, that looks like a reverse to the wellknown Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal. Mathematics subject classification (2010): 42A16, 42A38, 42B20.