Related papers: Explicit quadratic large sieve inequality
We present Hermite--Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on simplices
The classical Hormander's inequality for linear partial differential operators with constant coeffcients is extended to pseudodifferential operators.
Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in \cite{PSMA2016}. As…
By providing a variant of Weyl's inequality for general systems of forms we establish the Hardy-Littlewood asymptotic formula for the density of integer zeros of systems of quadratic or cubics forms under weaker rank conditions than…
We study functional inequality of the form $$|T(f,h)-T(f,g)T(g,h)| \leq F(f,g)F(g,h) -F(f,h)$$ where $T$ is a complex-valued functional and $F$ is a real-valued map. Motivation for our studies comes from some generalizations of Gr\"uss…
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
We provide a new characterization of the logarithmic Sobolev inequality.
Hardy's inequality on $H^p$ spaces, $p\in(0,1]$, in the context of orthogonal expansions is investigated for general basis on a subset of $\mathbb{R}^d$ with Lebesgue measure. The obtained result is applied to various Hermite, Laguerre, and…
We establish sharp upper bounds on shifted moments of quadratic Dirichlet $L$-functions over function fields. As an application, we prove some bounds for moments of quadratic Dirichlet character sums over function fields.
We show a new large sieve version of the Brun-Titchmarsh theorem.
We survey a number of different methods for computing $L(\chi,1-k)$ for a Dirichlet character $\chi$, with particular emphasis on quadratic characters. The main conclusion is that when $k$ is not too large (for instance $k\le100$) the best…
We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and Faber-Krahn estimates for H\"{o}rmander vector fields.
The author introduces the concept of harmonically ({\alpha},m)-convex functions and establishes some Hermite-Hadamard type inequalities of these classes of functions.
In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.
Heavy-quark effective theory (HQET) is applied to lattice QCD with Wilson fermions at fixed lattice spacing a. This description is possible because heavy-quark symmetries are respected. It is desirable because the ultraviolet cutoff $1/a$…
We survey quadratic Hessian equations: definition, background, rigidity of entire solutions, regularity of viscosity solutions, a priori Hessian estimates, and open problems.
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated…
The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic…