Related papers: An Ohsawa-Takegoshi-type $L^2$ extension for upper…

The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…

In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.

This paper investigates continuity properties of value functions and solutions for parametric optimization problems. These problems are important in operations research, control, and economics because optimality equations are their…

The approximation of integral type functionals is studied for discrete observations of a continuous It\^o semimartingale. Based on novel approximations in the Fourier domain, central limit theorems are proved for $L^2$-Sobolev functions…

A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a…

We give a general method for constructing examples of transcendental entire functions of given small order, which allows precise control over the size and shape of the set where the minimum modulus of the function is relatively large. Our…

We construct a functional model (direct integral expansion) and study the spectra of certain periodic block-operator Jacobi matrices, in particular, of general 2D partial difference operators of the second order. We obtain the upper bound,…

In this paper, we prove a version of the typed B\"ohm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a…

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $ \int_{\gamma}…

We extend in this article the classical Sobolev inequalities for the module of continuity for the functions belonging to the integer order Sobolev's space on the Sobolev-Bilateral Grand Lebesgue spaces. As a consequence, we deduce the…

In this article, we get properties for singular (dual) Nakano semi-positivity and obtain singular type vanishing theorem involving $L^2$-subsheaves on weakly pseudoconvex manifolds by $L^2$-estimates and $L^2$-type Dolbeault isomorphisms.…

We prove results on the relaxation and weak* lower semicontinuity of integral functionals of the form \[ \mathcal{F}[u] := \int_{\Omega} f \bigg( \frac{1}{2} \bigl( \nabla u(x) + \nabla u(x)^T \bigr) \bigg)\,\mathrm{d} x, \qquad u : \Omega…

We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…

We study integration and $L^2$-approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor product of univariate Hermite spaces and the probability measure…

We consider an $L^2$-Wasserstein type distance $\rho$ on the configuration space $\Gamma_X$ over a Riemannian manifold $X$, and we prove that $\rho$-Lipschitz functions are contained in a Dirichlet space associated with a measure on…

In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space $H^{m}(\Omega)$, where $\Omega$ is any bounded, smooth, open subset of $\mathbb{R}^{2m}$, $m\ge 1$. Moreover, we extend…

For the purpose of proving the strong openness conjecture of multiplier ideal sheaves, Jonsson-Musta\c{t}\u{a} posed an enhanced conjecture and proved the two-dimensional case, which says that: the Lebesgue measure of the set…

We study the asymptotics of Ohsawa-Takegoshi extension operator and orthogonal Bergman projector associated with high tensor powers of a positive line bundle. More precisely, for a fixed complex submanifold in a complex manifold, we…

Let $\Sigma$ be a strictly convex, compact patch of a $C^2$ hypersurface in $\mathbb{R}^n$, with non-vanishing Gaussian curvature and surface measure $d\sigma$ induced by the Lebesgue measure in $\mathbb{R}^n$. The Mizohata--Takeuchi…

We prove a theorem on the extension of holomorphic sections of powers of adjoint bundles from submanifolds of complex codimension 1 having non-trivial normal bundle. The first such result, due to Takayama, considers the case where the…