Related papers: Characteristic functions as bounded multipliers on…

We study various regularity properties of minimizers of the $\Phi$--perimeter, where $\Phi$ is a norm. Under suitable assumptions on $\Phi$ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is…

In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality, and obtain $L^1$…

We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…

We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.

We characterize Banach spaces B of stable type p (1 < p < 2) by the property that for every sequence (X_i) of B-valued random variables, independent, centered and fulfilling some integrability assumption, the sequence S_n/n^(1/p) is a…

We consider a scale invariant functional involving the anisotropic $p-$momentum, the anisotropic perimeter and the volume. We show that the Wulff shape, associated with the Finsler norm $F$ considered and centered at the origin, is the…

This paper investigates the existence, nonexistence, and qualitative properties of p-harmonic functions in the upper half-space $\mathbb{R}^N_+ \, (N \geq 3)$ satisfying nonlinear boundary conditions for $1<p<N$. Moreover, the symmetry of…

The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality,…

We prove a Fatou type theorem for bounded functions with d_J -bar differential of a controled growth on smoothly bounded domains in an almost complex manifold.

For an $(n\ge 2)$-dimensional real Banach space $E$ with unit ball $E_{\le 1}$ and a topological space $X$ arbitrary elements in $C(X,E_{\le 1})$ are always expressible as linear combinations of at most three functions valued in the unit…

In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…

We investigate several boundedness properties of function spaces considered as uniform spaces.

A function between two metric spaces is said to be totally bounded regular if it preserves totally bounded sets. These functions need not be continuous in general. Hence the purpose of this article is to study such functions vis-\'a-vis…

We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…

We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of…

We show that for a very wide class of Banach spaces of functions on [0,1] there are intrinsic lower bounds for the essential spectral radius of the transfer operator associated to piecewise smooth expanding maps. The class of Banach spaces…

Let $X$ and $Y$ be Banach spaces and $(\Omega,\Sigma,\mu)$ a finite measure space. In this note we introduce the space $L^p[\mu;L(X,Y)]$ consisting of all (equivalence classes of) functions $\Phi:\Omega \mapsto L(X,Y)$ such that $\omega…

Given any smooth Anosov map we construct a Banach space on which the associated transfer operator is quasi-compact. The peculiarity of such a space is that in the case of expanding maps it reduces exactly to the usual space of functions of…

We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses and on the regularity of the solutions to the associated…

In their 1976 paper, Nagel and Rudin characterize the closed unitarily and M\"obius invariant spaces of continuous and $L^p$-functions on a sphere, for $1\leq p<\infty$. In this paper we provide an analogous characterization for the…