We compute the Hausdorff dimension of sets of very well approximable vectors on rational quadrics. We use ubiquitous systems and the geometry of locally symmetric spaces. As a byproduct we obtain the Hausdorff dimension of the set of rays with a fixed maximal singular direction, which move away into one end of a locally symmetric space at linear depth, infinitely many times.

In this paper the boundedness for a large class of multisublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calderón-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

Let Γ be a finitely generated, torsion-free, two step nilpotent group. Let C(Γ) be the universal C∗-algebra of Γ. We show that acsr(C∗(Γ)) = acsr(C((Γ̂)1), where for a unital C∗-algebra A, acsr(A) is the absolute connected stable rank of A, and where (Γ̂)1 is the space of one-dimensional representations of Γ. For the case of stable rank, we have close results. In the process, we give a stable ran...

We establish the maximal regularity for nonautonomous OrnsteinUhlenbeck operators in L-spaces with respect to a family of invariant measures, where p ∈ (1,+∞). This result follows from the maximal L-regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on L(R ) with Lebesgue measure.

The aim of this paper is to study semigroups possessing E-regular elements, where an element a of a semigroup S is E-regular if a has an inverse a◦ such that aa◦, a◦a lie in E ⊆ E(S). Where S possesses ‘enough’ (in a precisely defined way) E-regular elements, analogues of Green’s lemmas and even of Green’s theorem hold, where Green’s relations R,L,H and D are replaced by R̃E , L̃E , H̃E and D̃E . N...

We prove L estimates for the maximal Riesz transform in terms of the Riesz transform itself, for 1 < p ≤ ∞. We show that the corresponding weak L1 estimate fails for the maximal Riesz transform, but surprisingly does hold for the maximal Beurling transform.

Let (X,μ) be a non-homogeneous space in the sense that X is a metric space equipped with an upper doubling measure μ. The aim of this paper is to study the endpoint estimate of the maximal operator associated to a Calderón-Zygmund operator T and the L boundedness of the maximal commutator with RBMO functions

Students are often suggested to provide feedback to teachers on lectures, learning materials and tests among other things. While such information can considerably improve the learning process it is necessary to find an effective way to obtain feedback and at the same time decrease the amount of time students use to deliver it. This article is a step towards extracting maximal knowledge with min...

We show that the maximal number of singular moves required to pass between any two regularly homotopic plane or spherical curves with at most n crossings grows quadratically with respect to n. Furthermore, for any two regularly homotopic curves with at most n crossings, there exists such a sequence of singular moves, satisfying the quadratic bound, for which all curves along the way have at mos...

Jech and Shelah [2] studied full reflection below אω, and produced a model in which the extent of full reflection is maximal in a certain sense. We produce a model in which full reflection is maximised in a different direction.