We give an explicit expression of the functions in the finite-dimensional coinvariant subspace of the Hardy and weighted Bergman spaces over the infinite polydisc. As an application, an alternative form of the Perfekt–Pushnitski theorem characterizing Hel

Consider spherical means on the Heisenberg group with a codimension 2 incidence relation, and associated spherical local maximal functions $M_E f$ where the dilations are restricted to a set $E$. We prove $L^p\to L^q$ estimates for these maximal operators

This paper is devoted to the study of the broad problem of deriving global metric properties from local quasiconformality in metric spaces. In particular, we show that, under certain regularity and connectivity conditions, a quasiconformal map between met

In this article, an analogue $h^S_{\rm top}$ of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of $h^S_{\rm top}$, including the existence of the limit in the definition, its relationship to topological entr

We prove that convex functions on a $C_b(X)$ space satisfying a mild continuity condition can be represented using $\sigma $-additive measures. This generalises a result of Cheridito, Kupper and Tangpi [Studia Math. 260 (2021), 121–140].

For a commutative unital ring $R$, and $n\in \mathbb N$, let $\mathrm{SL}_n(R)$ denote the special linear group over $R$, and $\mathrm E_n(R)$ the subgroup of elementary matrices. Let $\mathcal M^+$ be the Banach algebra of all complex Borel measures on $

We investigate quasidiagonality of weighted shifts on directed trees. We concentrate mainly on a subclass of weighted shifts operators called adjacency operators. In particular, we provide equivalent conditions for quasidiagonality of adjacency operators in terms of the structure of directed trees.

We study the family of closed sets of (extended) uniqueness of a locally compact group $G$ which is not necessarily abelian. We prove some preservation properties concerning this family of sets as well as their operator-theoretic counterpart, locate their

We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for the intrinsic

We investigate the relationship between the compactness of embeddings of Sobolev spaces built upon rearrangement-invariant spaces into rearrangement-invariant spaces endowed with $d$-Ahlfors measures under certain restriction on the speed of their decay o