Harnack type inequality and a priori estimates for solutions of a class of semilinear elliptic equations

For dimensions 3?n?6, we derive here the Harnack type inequality

     

Generalized Bebiano-Lemos-Providência inequalities and their reverses

We improve Bebiano-Lemos-Providência inequality: For A,B?0

     

Improved Poincaré inequalities with weights

In this paper we prove that if Ω∈Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:

     

Some functional inverse Santaló inequalities

Let be a log-concave function and for z∈Rn, define

     

Liouville type theorems for the system of integral equations

Consider the system of integral equations in Rⁿ

     

A Cohen type inequality for Laguerre-Sobolev expansions

Let introduce the Sobolev type inner product

     

Converse theorem for the Minkowski inequality

Let (Ω,Σ,μ) a measure space such that 0<μ(A)<1<μ(B)<∞ for some A,B∈Σ. Under some natural conditions on the bijective functions φ,φ₁,φ₂,ψ,ψ₁,ψ₂:(0,∞)→(0,∞) we prove that if

     

A sharp Hardy-type inequality of Sugeno integrals

This paper improves on previous work presenting a Hardy-type inequality for Sugeno integrals. Indeed, we show that for (S)_∫Df(x)dx?1,

     

A new hybrid iterative algorithm for variational inequalities

Let H be a real Hilbert space. Let F:H→H be a strongly monotone and Lipschitzian mapping. Let be an infinite family of non-expansive mappings with common fixed points set . We devise an iterative algorithm

     

A system of integral equations on half space

Let be the n-dimensional upper half Euclidean space, and let α be any real number satisfying 0<α<n, we study positive solutions of the following system of integral equations in :

     

Duality techniques for certain integral transforms to be starlike

For β<1, let denote the class of all normalized analytic functions f such that

     

Isolated singularities of polyharmonic inequalities

We study nonnegative classical solutions u of the polyharmonic inequality

     

Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls

For 0?σ<1/2 we characterize Carleson measures μ for the analytic Besov-Sobolev spaces on the unit ball Bn in Cn by the discrete tree condition

     

Precise rates in the law of the logarithm in the Hilbert space

Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X₁+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,

     

The generalized Roper-Suffridge extension operator for some biholomorphic mappings

Suppose f is a spirallike function of type β (or starlike function of order α) on the unit disk D in C. Let , where 1?p₁?2 (or 0<p₁?2), pj?1, j=2,…,n, are real numbers. In this paper, we prove that

     

Up-to boundary regularity for a singular perturbation problem of p-Laplacian type

In this paper we are interested in establishing up-to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular/degenerate elliptic operator. Our main result states: if Ω⊂Rn is a C1,α domain, for some 0<α<1 and uε verifies

     

Convolution of discrete measures on linear groups

Let p,q∈R such that 1<p<2 and . Define

(∗)