Related papers: Some remarks on extremal problems in weighted Berg…

For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…

This paper studies the strong quasiconvexity of norm and distance functions in finite-dimensional normed spaces. Although the Euclidean norm is known to be strongly quasiconvex on bounded convex sets, a complete characterization of this…

In this survey we collect some recent advances concerning embedding theorems in analytic and harmonic function spaces of several variables in various domains in $C^n.$ Some sharp embedding results presented in this survey paper extend sharp…

Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube $[0,1]^m$, $m\geq 2$. In this paper, we study a class of extremal problems that is closely connected to the…

In this paper, we unify and improve existing results on characterizing strict and almost stricty convex functions via subdifferential mapping, Moreau envelope, and proximal mappings. In particular, it is shown that if a convex function is…

We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…

In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice…

We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.

For a pseudoconvex tube domain, we prove estimates that relate the sublevel sets of its diagonal Bergman kernel to the floating bodies of its convex base. This allows us to associate a new affine invariant to any convex body.

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…

We show that weighted Bergman projections corresponding to radially symmetric weights on the unit disc are bounded on Sobolev spaces.

We contruct two classes of Zalcman-type domains, on which the Bergman distance functions have certain pre-described boundary behaviors. Such examples also lead to generalizations of uniformly perfectness in the sense of Pommerenke. These…

We show that on smooth complete Reinhardt domains, weighted Bergman projection operators corresponding to exponentially decaying weights are unbounded on $L^p$ spaces for all $p\not=2$. On the other hand, we also show that the exponentially…

In this paper we give sharp norm estimates for the Bergman operator acting from weighted mixed-norm spaces to weighted Hardy spaces in the ball, endowed with natural norms.

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…

We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of…

We show that a smooth bounded domain in $\mathbb{C}^n$ admitting partial pseudoconvex exhaustion remains partial pseudoconvex. The main ingredient of the proof is based on a new characterization of hyper-$q$-convex domains. Furthermore, we…

We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to integral approximation). The…

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone…