Related papers: A note on Hardy $q$-inequalities
We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and…
We study finite sections of weighted Hardy's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.
A simple proof of the weighted two variable geometric-arithmetic a mean inequality based on one given earlier valid only for integer weights
We give a new simpler proof of a theorem of Jayne and Rogers.
We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.
We give a very short proof of the Golden-Thompson inequality
We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.
We correct a mistake in the paper ["On weighted iterated Hardy-type inequalities", Positivity, 22 (1) (2018), 275-299]. -- In this paper the inequality $$ \bigg( \int_0^{\infty} \bigg( \int_x^{\infty} \bigg( \int_t^{\infty} h \bigg)^q…
We improve the classical discrete Hardy inequality for $ 1<p<\infty $ for functions on the natural numbers. For integer values of $ p $ the Hardy weight is an absolutely monotonic function.
We prove the self-improvement of a pointwise $p$-Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.
In this paper we prove sharp Hardy inequalities by using Maximal function theory. Our results improve and extend the well-known results of G.Hardy \cite{Ha04}, T.Cazenave \cite {Ca03}, J.-Y.Chemin\cite {Ch06} and T.Tao\cite {TT06}.
In this work we improve the sharp Hardy inequality in the case $p>n$ by adding an optimal weighted Hoelder semi-norm. To achieve this we first obtain a local improvement. We also obtain a refinement of both the Sobolev inequality for $p>n$…
We prove Burkholder inequality using Bregman divergence.
In this paper, we give a simple counter example to the famous Hodge conjecture.
We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…
In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
In this paper, we prove a sharp, weighted Hardy-type inequality for the Dirac operator. A key feature of our result is that the inequality is not only sharp but also attained, and we construct explicit minimizers that satisfy the equality…
In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].
In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series…