Let f be a non-negative function on R, which is radially monotone (0 < f ↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup f↓r ∫ Rn fg (∫ Rn f pv ) 1 p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given.

This note studies the relationship between Hutton's quasi-uniformities and Shi's quasi-uniformities. It is shown that when $L$ satisfies``multiple choice principle" for co-prime elements, the category of Hutton's quasi-uniform spaces is a bireflective full subcategory of the category of Shi's quasi-uniform spaces. Especially, if the remote-neighborhood mapping defined by Shi preserves arbitrary...

We establish a general “boundedness implies convergence” principle for family of evolving Riemannian metrics. then apply this to collapsing Calabi–Yau metrics and normalized Kähler–Ricci flows on minimal models obtain convergence results.

Abstract. We study the uniform nonsingularity property recently proposed by the authors and present its applications to nonlinear complementarity problems over a symmetric cone. In particular, by addressing theoretical issues such as the existence of Newton directions, the boundedness of iterates and the nonsingularity of B-subdifferentials, we show that the non-interior continuation method pro...

In this paper we propose anti surge controllers for a close coupled valve in a compression system. The valve modifies the characteristic of the compressor, and allows for stable operation beyond the original surge line. The design tool used is backstepping and global uniform asymptotic stability is proven. Damping terms are included in the controllers, and in the presence of both mass flow and ...

We give conditions on a strongly continuous semigroup T and a bounded perturbation B such that the perturbed semigroup S preserves asymptotic properties as boundedness, asymptotic almost periodicity, uniform ergodicity and total uniform ergodicity. In the rst systematic treatise on perturbation of semigroups, R.S.Phillips 10] proved in 1953 that, if A is the innnitesimal generator of a strongly...

Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As an application, we construct approximations for the timedependent Stokes equations with a source term in L(0, T ;L(Ω)) and prove uniform estimates on the time derivative and di...

In this paper, a novel adaptive visual feedback scheme is presented to solve the problem of controlling the relative pose between a robot camera and a rigid object of interest. By exploiting nonlinear controllability properties, uniform asymptotic stability in the large of the image reference set-point is proved using Lyapunov’s direct method. Moreover, uniform boundedness of the whole state ve...

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and th...

Since the theory of pseudo-differential operators was established in 1970’s, the L-boundedness of them with symbols in the Hörmander class S ρ,δ has been well investigated by many authors. Among them, Calderón-Vaillancourt [5] first treated the boundedness for the class S 0,0, which means that the boundedness of all the derivatives of symbols assures the L-boundedness of the corresponding opera...