Related papers: The double difference property for the class of lo…

We prove the validity of regularizing properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with…

We study the class of affine self-similar and continuous on interval $[0;1]$ functions. Formulas for the H\"{o}lder exponents are obtained in terms of self-similarity parameters.

We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and unbounded Hessian. The same construction is also applicable to higher order differentiability.

In this paper, we introduce and investigate a class P of continuous and periodic functions on R. The class P is defined so that second-order central differences of a function satisfy some concavity-type estimate. Although this definition…

Local oscillation of a function satisfying a H\"older condition is considered and it is proved that its growth is governed by a version of the Law of the Iterated Logarithm.

The goal of this note is to give an alternative proof of local H\"older continuity for functions in DeGiorgi classes based on an idea of Moser.

In this article, we consider derivatives of local time for a $(2,d)$-Gaussian field \[ Z=\big\{ Z(t,s)= X^{H_1}_t -\widetilde{X}^{H_2}_s, s,t \ge 0\big\}, \] where $X^{H_1}$ and $\widetilde{X}^{H_2}$ are two independent processes from a…

We give a proof of the Howe duality conjecture in local theta correspondence for symplectic-orthogonal or unitary dual pairs in arbitrary residual characteristic.

We give a proof for the H\"older continuity of functions in the parabolic De Giorgi classes in metric measure spaces. We assume the measure to be doubling, to support a weak $(1,p)$-Poincar\'e inequality and to satisfy the annular decay…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

We separate the local diameter two property from the diameter two property and their weak-star counterparts from each other in spaces of Lipschitz functions. We characterise the $w^*$-LD$2$P, the $w^*$-D$2$P, the LD$2$P, and the SD$2$P in…

This paper deals with the embedding of the Sobolev spaces of fractional order into the space of H\"older continuous functions. More precisely, we show that the function $f\in H^s(\mathbb{R})$ with $\frac{1}{2}<s<1$ is H\"older continuous…

We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded Hessian. The same construction is also applicable to higher order differentiability, the Monge-Amp\`ere equation, and mean…

The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…

It is shown that the Bishop-Phelps-Bollob\'as theorem holds for bilinear forms on the complex $C_0(L_1)\times C_0(L_2)$ for arbitrary locally compact topological Hausdorff spaces $L_1$ and $L_2$.

We address a classical open question by H.Brezis and R.Ignat concerning the characterization of constant functions through double integrals that involve difference quotients. Our first result is a counterexample to the question in its full…

We show that the space of bounded and linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollob\'as property. A similar result is also proved for the class of compact…

In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs from the set-theoretic one. Here we…

A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved.

We prove local H\"older continuity for non negative, locally bounded, local weak solutions to the class of doubly nonlinear parabolic equations $\partial_t (u_q) - \text{div} (|Du|^{p-2} Du) = 0$ for $p > 2$, $ 0 < q < p-1$. The proof…