Related papers: A note on Hardy $q$-inequalities

We study the fractional Hardy inequality on the integers. We prove the optimality of the Hardy weight and hence affirmatively answer the question of sharpness of the constant.

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…

We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions…

In this paper we study some improvements of the classical Hardy inequality. We add to the right hand side of the inequality a term which depends on some Lorentz norms of $u$ or of its gradient and we find the best values of the constants…

In this note I give an information-theoretic proof of the Bonami-Beckner-Gross hypercontractive inequality.

This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…

In this paper,we will give an easy example to satisfy that we can not conclude CDE' Inequality just from the CD Inequality.

In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the…

We study Hardy type inequalities involving mixed cylindrical and spherical weights, for functions supported in cones. These inequalities are related to some singular or degenerate differential operators.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

In this paper, we present a short proof of Halin's grid theorem.

We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some L\'evy processes, and weighted fractional inequalities on irregular open…

We prove a stability version of the Pr\'ekopa-Leindler inequality.

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

In this note we present a version of Hardy's inequality on a measure space $(X,\mu)$ endowed with a measurable function $N\colon X\to \mathbb R$ which replaces the absolute value on $\mathbb R$ or $\mathbb R^n$, and, more generally, the…

We revisit and slightly modify the proof of the Gaussian Hanson-Wright inequality where we keep track of the absolute constant in its formulation.

We present inequalities and some applications to Kellers' limit and Carlemans' inequality.

Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's…

We extend the work of Dyda and Kijaczko by establishing the corresponding weighted fractional Hardy inequalities with singularities on any flat submanifolds. While they derived weighted fractional Hardy inequalities with singularities at a…