Related papers: On Khintchine inequalities with a weight

In this paper, we prove some inequalities for the differences and ratios of the beta function.

The aim of this paper is to provide a proof for a version of Morse inequality for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof…

In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions.

We give a new characterization of the two weight inequality for a vector-valued positive operator. Our characterization has a different flavor than the one of Scurry's and H\"{a}nninen's. The proof can be essentially derived from the…

We prove a weighted version of the Hardy-Littlewood-Sobolev inequality for radially symmetric functions, and show that the range of admissible power weights appearing in the classical inequality due to Stein and Weiss can be improved in…

A treatment of (generalized) Clemens-Schmid exact sequences from the perspective of weights.

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

In this note, we prove a family of sharp weighed inequality which involves weighted $k$-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in $\mathbb{R}^n$. This inequality generalizes the corresponding…

In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed.

In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved

This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…

In this work we provide the best constants of the multiple Khintchine inequality. This allows us, among other results, to obtain the best constants of the mixed $\left( \ell_{\frac{p}{p-1}},\ell_{2}\right) $-Littlewood inequality, thus…

Functions that satisfy the Hadamard Fisher Inequalities also satisfy Newton's Inequalities

In this paper, some new Gronwall type inequalities involving iterated integrals are given.

In [6] we proved Chen's inequality regarded as a problem of constrained maximum. In this paper we introduce a Riemannian invariant obtained from Chen's invariant, replacing the sectional curvature by the Ricci curvature of k-order. This…

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…

By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.

We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…