Related papers: Functional boundedness of balleans

Some boundedness properties of function spaces (considered as topological groups) are studied.

We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic…

We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.

We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…

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

This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…

We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.

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…

We develop a coarse notion of bundle and use it to understand the coarse geometry of group extensions and, more generally, groups acting on proper metric spaces. The results are particularly sharp for groups acting on (locally finite) trees…

Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…

We prove that bounded conciseness is a closed property in the space of marked groups. As a consequence, we reformulate a conjecture of Fern\'andez-Alcober and Shumyatsky [7] about conciseness in the class of residually finite groups.

We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses…

We study the boundary behaviour of a variant of the Fridman's invariant function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in $ \mathbb{C}^n $ and…

This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$.

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

A ballean (or coarse structure) is a set endowed with some family of subsets, the balls, is such a way that balleans with corresponding morphisms can be considered as asymptotic counterparts of uniform topological spaces. For a ballean…

We study bounded domains with certain smoothness conditions and the properties of their squeezing functions in order to prove that the domains are biholomorphic to the ball.

Assuming that $S$ is the space of functions of regular variation, $\omega\in S$, $0< p<\infty$, a function $f$ holomorphic in $B^n$ is said to be of Besov space $B_p(\omega)$ if $$\|f\|^p_{B_p(\omega )}=\int_{B^n}…

We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.

We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…