Related papers: Particle systems, Dipoles and Besov spaces of dist…
The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum…
Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of…
We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.
The aim of this paper is to study properties of Besov-type spaces with variable smoothness. We show that these spaces are characterized by the phi-transforms in appropriate sequence spaces and we obtain atomic decompositions for these…
We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products.…
This paper considers coorbit spaces parametrized by mixed, weighted Lebesgue spaces with respect to the quasi-regular representation of the semi-direct product of Euclidean space and a suitable matrix dilation group. The class of dilation…
We introduce new quantitative measures for cyclicity in radially weighted Besov spaces, including the Drury-Arveson space, by defining cyclicity indices based on potential theory and capacity. Extensions to non-commutative settings are…
This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…
We introduce a family of quasi-Banach spaces - which we call wave packet smoothness spaces - that includes those function spaces which can be characterised by the sparsity of their expansions in Gabor frames, wave atoms, and many other…
This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish the stability and convergence of a semi-implicit time-stepping…
We establish conditions on the parameters which are both necessary and sufficient in order that Besov and Triebel-Lizorkin spaces of generalized smoothness contain only regular distributions. We also connect this with the possibility of…
Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized…
In spaces of metrics, we investigate topological distributions of the doubling property, the uniform disconnectedness, and the uniform perfectness, which are the quasi-symmetrically invariant properties appearing in the David--Semmes…
In this paper, we generalize classic mass partition results dealing with partitions using spheres, parallel hyperplanes, or axis-parallel wedges to the setting of mass assignments. In a mass assignment problem, we assign mass distributions…
This paper is concerned with the study of Besov-type decomposition spaces, which are scales of spaces associated to suitably defined coverings of the euclidean space $\mathbb{R}^d$, or suitable open subsets thereof. A fundamental problem in…
We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a…
We introduce a decoupling method on the Wiener space to define a wide class of an\-iso\-tro\-pic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov…
We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces $Z$. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices $s<1,$ as well as the first order…
We use Littlewood-Paley-Stein type g-functions (also called generalized square functions) associated to symmetric diffusion semigroups to obtain a characterization of inhomogeneous abstract Besov spaces on the abstract Hilbert spaces. Then…
We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is…