Related papers: An interpolation proof of Ehrhard's inequality
We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many…
We present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the…
We give the connections among the Fekete sets, the zeros of orthogonal polynomials, $1(w)$-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fej\'er contants. Finally the convergence of a…
To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…
We give a multivariate generalization of Borell's noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process.
Extensions and generalizations of Alzer's inequality; which is of Wirtinger type are proved. As applications, sharp trapezoid type inequality and sharp bound for the geometric mean are deduced.
We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.
In this paper we study a family of interpolation Gagliardo-Nirenberg-Sololev inequalities on planar graphs. We are interested in knowing when the best constants in the inequalities are achieved. We also analyse the set of solutions of the…
For any lattice polytope $P$, we consider an associated polynomial $\bar{\delta}_{P}(t)$ and describe its decomposition into a sum of two polynomials satisfying certain symmetry conditions. As a consequence, we improve upon known…
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
In this note, we give a new proof of subcritical Trudinger-Moser inequality on $\mathbb{R}^n$. All the existing proofs on this inequality are based on the rearrangement argument with respect to functions in the Sobolev space…
Bernstein-Nikolskii inequalities and Riesz interpolation formula are established for eigenfunctions of Laplace operators and polynomials on compact homogeneous manifolds.
We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients,…
Ehrhart polynomials are extensively-studied structures that interpolate the discrete volume of the dilations of integral $n$-polytopes. The coefficients of Ehrhart polynomials, however, are still not fully understood, and it is not known…
We prove some extensions of Andrews inequality.
We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.
We prove a general independent equidistribution result for Gauss sums associated to $n$ monomials in $r$ variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and…
We determine the poles of maximal unramified degenerate Eisenstein series of a split semisimple algebraic group over a number field using a straightforward global argument, avoiding delicate analysis of intertwining operators.
Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…