Related papers: A note on multiple summing operators and applicati…
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
In this short note we obtain new lower bounds for the constants of the real Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}^{2}$ spaces when $p=2m$ and for certain values of $m$. The real and complex cases for the general…
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.
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…
We introduce a general multisummability theory of formal power series in Carleman ultraholomorphic classes. The finitely many levels of summation are determined by pairwise comparable, nonequivalent weight sequences admitting nonzero…
We consider the space of molecules endowed with the transpose version of the Chevet-Saphar norm and we identify its dual space with the space of Lipschitz strongly p-summing operators. We also extend some old results to the category of…
We prove bounds for multilinear operators on $\R^d$ given by multipliers which are singular along a $k$ dimensional subspace. The new case of interest is when the rank $k/d$ is not an integer. Connections with the concept of {\em true…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
The best known upper estimates for the constants of the Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}$ spaces are of the form $\left(\sqrt{2}\right) ^{m-1}.$ We present better estimates which depend on $p$ and $m$. An…
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain new criteria equivalent to the Riemann hypothesis. Later, the same theorem was applied…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying…
We establish nontrivial bounds for bilinear sums involving the M\"obius function evaluated over solutions to a broad class of equations. Several of our results may be regarded as M\"obius-function analogues of the ternary Goldbach problem.…
We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea. We show that this also adapts to give some new sieve inequality for modular…
Strengthening of two Clarkson-McCarthy inequalities with several operators is established. These not only confirm a conjecture of the author in [Israel J. Math. 2024], but also improve results of Hirazallah-Kittaneh in [Integral Equations…
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between…
In this work, a pre-Gr\"{u}ss inequality for positive Hilbert space operators is proved. So that, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound…
In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.