We obtain a reverse Hölder inequality for the eigenfuctions of Schrödinger operator with slowly decaying potentials. The class potentials includes singular which decay like $$|x|^{-\alpha }$$ $$0<\alpha <2$$ , in particular Coulomb potential.

In this paper we discuss the global weak sharp minima property for vector optimization problems with polynomial data. Exploiting the imposed polynomial structure together with tools of variational analysis and a quantitative version of Lojasiewicz’s gradient inequality due to D’Acunto and Kurdyka, we establish the Hölder type global weak sharp minima with explicitly calculated exponents.

We investigate a convex function ψp,q,λ = max{ψp, λψq}, (1 ≤ q < p ≤ ∞), and its corresponding absolute normalized norm ‖.‖ψp,q,λ . We determine a dual norm and use it for getting refinements of the classical Hölder inequality. Also, we consider a related concave function φp,q,λ = min{ψp, λψq}, (0 < p < q ≤ 1).

In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The investigated here generalize several known scales and unify extend continuous their corresponding discrete analogues. Our results will be proved by using algebraic inequalities, Hölder inequality, Jensen’s inequality

We prove a sharp Hölder estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has unit determinant. Our result extends some previous work by Piccinini and Spagnolo [7]. The proof relies on a sharp Wirtinger type inequality.

We establish various Lp estimates for the Schrödinger operator −∆ + V on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where ∆ is the Laplace-Beltrami operator and V belongs to a reverse Hölder class. At the end of this paper we apply our result on Lie groups with polynomial growth.

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...

We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of strengthened CauchySchwarz inequalities is derived using these identities. Also, an analogous version of this result is given for strengthened Hölder inequalities.

In this paper, we will prove some new dynamic inequalities on a time scale T . These inequalities when T = N contain the discrete inequalities due to Bennett and Leindler which are converses of Copson’s inequalities. The main results will be proved using the Hölder inequality and Keller’s chain rule on time scales. Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40. 34...

Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be Hölder continuous, with a modulus depending only on the growth of the Hamiltonian. The proof involves some representation formula for nonlocal Hamilton-Jacobi equations in terms of controlled jump processes and a weak reverse inequality.