We show that the lowest constant appearing in the weak type (1,1) inequality satisfied by the centered Hardy-Littlewood maximal operator on radial integrable functions is 1.

We perform a convergence analysis for discretization of Helmholtz scattering and resonance problems obtained by Hardy space infinite elements. Super-algebraic convergence with respect to the number of Hardy space degrees of freedom is achieved. As transparent boundary spheres and piecewise polytopes are considered. The analysis is based on a G̊arding-type inequality and standard operator theoret...

In this paper, we will prove several new inequalities of Hardy type with explicit constants. The main results will be proved using generalizations of Opial's inequality.

In the euclidean space, Sobolev and Hardy-Littlewood-Sobolev inequalities can be related by duality. In this paper, we investigate how to relate these inequalities using the flow of a fast diffusion equation in dimension d ≥ 3. The main consequence is an improvement of Sobolev’s inequality when d ≥ 5, which involves the various terms of the dual Hardy-Littlewood-Sobolev inequality. In dimension...

0

let and be a sequence with non-negative entries. if , denote by the infimum of those satisfying the following inequality: whenever . the purpose of this paper is to give an upper bound for the norm of operator t on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). we considered this problem for certain matrix operators such as norlund, weighted mean, ceasaro and copson matrices. th...

Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and the...

In this paper, a theorem related to the Hilbert-type inequality is corrected. By introducing parameters, and using Euler-Maclaurin summation formula, we give a discrete form of the Hilbert-type inequality involving a non-homogeneous kernel. Furthermore, we prove that our result is a concise generalization of the corrected theorem and some known results. As applications, some particular new resu...

We give improvements and generalizations of both the classical Hardy inequality geometric based on divergence theorem. Especially, our improved type derives two inequalities with best constants. Besides, we improve Rellich by using inequality.

For a bounded linear operator A on a Hilbert space  , let ( ) M A be the smallest possible constant in the inequality ( ) ( ) ( ) p p D A M A R A ≤ . Here, p is a point on the smooth portion of the boundary ( ) W A ∂ of the numerical range of A. ( ) p R A is the radius of curvature of ( ) W A ∂ at this point and ( ) p D A is the distance from p to the spectrum of A. In this paper, we compute t...