Related papers: On Choquet integrals and pointwise estimates
One of the most natural and challenging issues in discrete complex analysis is to prove the convergence of discrete holomorphic functions to their continuous counterparts. This article is to solve the open problem in the general setting. To…
We establish some qualitative properties of minimizers in the fractional Hardy--Sobolev inequalities of arbitrary order.
In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is…
We present a local weighted estimate for the Riesz potential in $\mathbb{R}^n$, which improves the main theorem of Alberico, Cianchi, and Sbordone [C. R. Math. Acad. Sci. Paris \textbf{347} (2009)] in several ways. As a consequence, we…
In Dunkl theory on Rd which generalizes classical Fourier analysis, we study first the behavior at infinity of the Riesz potential of a non compactly supported function. Second, we give for 1<p<=q<infinite, weighted (Lp,Lq) boundedness of…
We consider the multigraded Hilbert scheme corresponding to the Hilbert function of a finite number of points in general position in a smooth projective complex toric variety. We develop several criteria for a point of that parameter space…
The purpose of this paper is to give a survey of a class of maximal inequalities for purely discontinuous martingales, as well as for stochastic integral and convolutions with respect to Poisson measures, in infinite dimensional spaces.…
We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results…
We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equipped with a volume form. We focus on Hardy-type inequalities…
We establish sharp trace- and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov…
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…
Problems pointwise estimates from above functions or its averages often arise in the function theory under known integral restrictions on the growth of this function. We offer an approach to such problems based on the integral Jensen's…
By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities induced by the embedding $\dot{H}^s({\mathbb R}^n)…
Consider a real valued function defined, but not differentiable at some point. We use sequences approaching the point of interest to define and study sequential concepts of secant and cord derivatives of the function at the point of…
\begin{abstract} Let $P\pm$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider estimates of the expression $\|( |P_ + f | ^s + |P_- f |^s) ^{\frac{1}{s}}\|_{L^p (\mathbf{T})}$ in terms of Lebesgue $p$-norm of the…
Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/\pi$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions…
We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.
We establish a Maz'ya type capacitary inequality which resolves a special case of a conjecture by David R. Adams. As a consequence, we obtain several equivalent norms for Choquet integrals associated to Bessel or Riesz capacities. This…