Related papers: Improving the Cauchy-Schwarz inequality
We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj\"orner--Wachs inequality and generalize it to inequalities on order polynomials and their $q$-analogues via direct…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
In this work I study the well-posedness of the Cauchy problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities}, which appears modeling problems in nonlinear optics. I obtain the local well-posedness for…
We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are…
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on…
This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…
Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the…
We derive sufficient conditions for the surjectivity of the Cauchy-Riemann operator $\overline{\partial}$ between spaces of weighted smooth Fr\'echet-valued functions. This is done by establishing an analog of H\"ormander's theorem on the…
In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the L\"owner-Heinz inequality,…
We propose probabilistic representations for inverse Stein operators (i.e. solutions to Stein equations) under general conditions; in particular we deduce new simple expressions for the Stein kernel. These representations allow to deduce…
Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
We present new results concerning the solvability, of lack thereof, in the Cauchy problem for the debar operator, with initial values assigned on a weakly pseudoconvex hypersurface, and provide illustrative examples.
This paper deals with spectral inequalities for one-dimensional Schr\"odinger operators with potentials bounded between two increasing functions (weights). The spectral inequality allows one to estimate the norm of a function with bounded…
Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators regularizing in all…
For exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carr\'e du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates…
In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for $N$-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence…
Group fairness in machine learning is often enforced by adding a regularizer that reduces the dependence between model predictions and sensitive attributes. However, existing regularizers are built on heterogeneous distance measures and…
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with…