In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator T to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing function...

Abstract. We consider a smooth two-parameter family fa,L : θ 7→ θ+a+LΦ(θ) of circle maps with a finite number of critical points. For sufficiently large L we construct a set A (∞) L of a-values of positive Lebesgue measure for which the corresponding fa,L exhibits an exponential growth of derivatives along the orbits of the critical points. Our construction considerably improves the previous on...

We compute point sets on the triangle that have low Lebesgue constant, with sixfold symmetries and Gauss-Legendre-Lobatto distribution on the sides, up to interpolation degree 18. Such points have the best Lebesgue constants among the families of symmetric points used so far in the framework of triangular spectral elements.

We study a class of Dirichlet boundary value problems whose prototype is [see formula in PDF] where 0 < p 1 and f belongs to suitable Lebesgue space. The main features this problem are the presence singular term | u ?2 datum which possibly changes its sign. introduce notion solution setting we prove an existence result for such solution. motivation our above due minimization non–differentiab...

Abstract We prove asymptotic stability of steady-state solutions to the Navier–Stokes equations in whole space. One novelties this work consists considering perturbations that show a distinct pointwise behavior (in space and time) correspond initial data only belonging suitable weighted Lebesgue spaces.