Differentiability of Musielak-Orlicz sequence spaces
Differentiability of the mappings of Carnot-Carathéodory spaces in the Sobolev and -topologies.
Differentiation bases for Sobolev functions on metric spaces.
We study Lebesgue points for Sobolev functions over other collections of sets than balls. Our main result gives several conditions for a differentiation basis, which characterize the existence of Lebesgue points outside a set of capacity zero.
Differentiation of Banach-space-valued additive processes
Dilatations des commutants d'opérateurs pour des espaces de Krein de fonctions analytiques
Soient et deux espaces de Krein de fonctions analytiques dans le disque unité invariants pour l’opérateur de déplacement à gauche et soit un opérateur linéaire continu de dans dont l’adjoint commute avec . Nous étudions les dilatations de qui conservent cette propriété de commutation et pour lesquelles les formes hermitiennes définies par et ont le même nombre de carrés négatifs. Nous obtenons ainsi une version du théorème de dilatation des commutants d’opérateurs dans le cadre...
Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces
We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the...
Dimensional compactness in biequivalence vector spaces
The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set and classes of set functions ...
Dimension-invariant Sobolev imbeddings
We survey recent dimension-invariant imbedding theorems for Sobolev spaces.
Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities
We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.
Direct Integrals of Hilbert Spaces II.
Discrepancy and integration in function spaces with dominating mixed smoothness [Book]
Discretization and anti-discretization of rearrangement-invariant norms.
Disjoint hypercyclic powers of weighted translations on groups
Let be a locally compact group and let Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space in terms of the weights. Sufficient and...
Disjoint strict singularity of inclusions between rearrangement invariant spaces
It is studied when inclusions between rearrangement invariant function spaces on the interval [0,∞) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions and to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.
Disjointification of martingale differences and conditionally independent random variables with some applications
Disjointification inequalities are proven for arbitrary martingale difference sequences and conditionally independent random variables of the form , where ’s are independent and xk’s are arbitrary random variables from a symmetric space X on [0,1]. The main results show that the form of these inequalities depends on which side of L₂ the space X lies on. The disjointification inequalities obtained allow us to compare norms of sums of martingale differences and non-negative random variables with...
Diskret kompakte Einbettungen in Sobolewschen Räumen.
Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann -function
It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plan free of zeros of the Riemann -function.
Distinguished preduals of spaces of holomorphic functions.
Distinguished subsets and complemented copies of C0 in vector sequence spaces.
Distinguished subspaces of of maximal dimension