The problem of the boundedness of the fractional maximal operator Mα, 0 ≤ α < n in local Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters.

We consider the gradient method xt+1 = xt + γt(st + wt), where st is a descent direction of a function f : �n → � and wt is a deterministic or stochastic error. We assume that ∇f is Lipschitz continuous, that the stepsize γt diminishes to 0, and that st and wt satisfy standard conditions. We show that either f(xt) → −∞ or f(xt) converges to a finite value and ∇f(xt) → 0 (with probability 1 in t...

In the above paper Chen et al. investigated the capability of uniformly approximating functions in C(Rn) by standard feedforward neural networks. They found that the boundedness condition on the sigmoidal function plays an essential role in the approximation, and conjectured that the boundedness of the sigmoidal function is a necessary and sufficient condition for the validity of the approximat...

We study Vector Addition Systems with States (VASS) extended in such a way that one of the manipulated integer variables can be tested to zero. For this class of system, it has been proved that the reachability problem is decidable. We prove here that boundedness, termination and reversal-boundedness are decidable for VASS with one zero-test. To decide reversal-boundedness, we provide an origin...

We study Vector Addition Systems with States (VASS) extended in such a way that one of the manipulated integer variables can be tested to zero. For this class of system, it has been proved that the reachability problem is decidable. We prove here that boundedness, termination and reversal-boundedness are decidable for VASS with one zero-test. To decide reversal-boundedness, we provide an origin...

In this paper we study the boundedness properties of certain oscillatory integrals with polynomial phase. We obtain sharp estimates for these oscillatory integrals. By the virtue of these estimates and extrapolation we obtain L boundedness for these oscillatory integrals under rather weak size conditions on the kernel function. Keywords—Fourier transform, oscillatory integrals, Orlicz spaces, B...

Wemake the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov-Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and ...

‎in this paper, using the idea of convexificators, we study boundedness and nonemptiness of lagrange multipliers satisfying the first order necessary conditions. we consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. within this context, define generalized mangasarian-fromovitz constraint qualification and show t...

in this paper, the stability and boundedness of solutions of a second order nonlinear vectordifferential equation are investigated. our results include and improve some well-known results in therelevant literature.