Related papers: Restricted testing conditions for the multilinear …
In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study the weighted boundedness. Motivated in the weighted boundedness of Hardy-Littlewood maximal studied by Antezana…
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality…
We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…
It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on…
The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data…
In this paper, based on the theory of adjoint operators and dual norms, we define condition numbers for a linear solution function of the weighted linear least squares problem. The explicit expressions of the normwise and componentwise…
We prove that the Hardy--Littlewood maximal operator $M$ is bounded on the variable Lebesgue space $L^{p(\cdot)}(X,d,\mu)$, with $1<p_-\le p_+<\infty$, over an unbounded space of homogeneous type $(X,d,\mu)$ with a Borel-semiregular measure…
Regularization robust preconditioners for PDE-constrained optimization problems have been successfully developed. These methods, however, typically assume that observation data is available throughout the entire domain of the state…
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…
We consider Lurye (sometimes written Lur'e) systems whose nonlinear operator is characterised by a possibly multivalued nonlinearity that is bounded above and below by monotone functions. Stability can be established using a sub-class of…
In this paper we obtain a new boundedness criterion for the maximal operator $M$ on variable exponent spaces $L^{p(\cdot)}$. It is formulated in terms of the variable exponent analogue of the well known weighted $A_{\infty}$ condition.
We characterize strong type and weak type inequalities with two weights for positive operators on filtered measure spaces. These estimates are probabilistic analogues of two-weight inequalities for positive operators associated to the…
In order to satisfy safety conditions, an agent may be constrained from acting freely. A safe controller can be designed a priori if an environment is well understood, but not when learning is employed. In particular, reinforcement learned…
It is a well known fact that finite time optimal controllers, such as MPC does not necessarily result in closed loop stable systems. Within the MPC community it is common practice to add a final state constraint and/or a final state penalty…
Some necessary and sufficient optimality conditions for inequality constrained problems with continuously differentiable data were obtained in the papers [I. Ginchev and V.I. Ivanov, Second-order optimality conditions for problems with…
In this note, we establish a discrete method to characterize the limiting weak type behaviors of the centered Hardy-Littlewood maximal operator on the positive real axis through testing on Dirac deltas. As an application, we give some new…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
In this paper we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator…