Related papers: A note on the Menchov-Rademacher Inequality
In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts. In the first part, we consider the following Caffarelli-Kohn-Nirenberg inequality:…
In this paper we establish the best constant $\widetilde A_{opt}(\bar{M})$ for the Trace Nash inequality on a $n-$dimensional compact Riemannian manifold in the presence of symmetries, which is an improvement over the classical case due to…
In this work, a refinement of the Cauchy--Schwarz inequality in inner product space is proved. A more general refinement of the Kato's inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical…
We establish some qualitative properties of minimizers in the fractional Hardy--Sobolev inequalities of arbitrary order.
In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.
Our main goal is to explicitly compute the best constant for the Sobolev-type inequality involving the polyharmonic operator obtained in (Analysis and Applications 22, pp. 1417-1446, 2024). To achieve this goal, we also establish both…
We shall give a refinement of the arithmetic-geometric mean inequality.
We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.
In this work, an extension of the generalized mixed Schwarz inequality is proved. A companion of the generalized mixed Schwarz inequality is established by merging both Cartesian and Polar decompositions of operators. Based on that some…
In this article we discuss a generalized Wirtinger inequality.
We establish Hanner's inequality for arbitrarily many functions in the setting where the Rademacher distribution is replaced with higher dimensional random vectors uniform on Euclidean spheres.
In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the…
We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).
In this note we give some remarks and improvements on a recent paper of us [3] about an optimization problem for the $p-$Laplace operator that were motivated by some discussion the authors had with Prof. Cianchi.
Let $M$ be a complete, simply connected Riemannian manifold with negative curvature. We obtain some Moser-Trudinger inequalities with sharp constants on $M$.
We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…
We obtain some results related to Romanoff's theorem.
Let S_n:=a_1\vp_1+...+a_n\vp_n, where \vp_1,...,\vp_n are independent Rademacher random variables (r.v.'s) and a_1,...,a_n are any real numbers such that a_1^2+...+a_n^2=1. Let Z be a standard normal r.v. It is proved that the best constant…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
Some extensions of an inequality from IMO'2001 are proven by means of the Lagrange multiplier criterion.