Mathematische Nachrichten最新文献

In this paper, we introduce five two-parameter $�B$-valued martingale Hardy–Lorentz–Karamata spaces and establish some atomic decomposition theorems via atomic martingales as well as atomic functions. With the aid of atomic decompositions, we obtain some martingale inequalities and characterize the duals of these spaces. Our conclusions strongly depend on the geometric properties of the underlying Banach spaces and remove the restrictive condition that the slowly varying function $�b$ is nondecreasing as in the previous literature.

In this paper, we are interested on the null controllability property of a linear degenerate Schrödinger equation with a degeneracy occurring on an interior subset of $���(�0�,�1�)��,��\text{that is,}��\exists �W_1�\subset �\subset ��(�0�,�1�)��,��\text{such that}��\forall �x�\in �W_1�,��k��\left(�x�\right)��=�0�$, where $�k$ stands for the quantum diffusion. More precisely, we are concerned with the null controllability phenomenon using the classical procedure founded on a new Carleman estimate and afterward a newfangled observability inequality.

Let $��X�=�G�/�K�$ be a symmetric space of the noncompact type. In this paper, we characterize joint eigenfunctions of $�G$-invariant differential operators on $�X$ through an asymptotic version of the generalized mean value property.

In this note, we show that special functions of bounded variation ($��\mathrm{SBV}�)�$ functions with jump normal lying in a prescribed set of directions $�N$ can be approximated by sequences of $�\mathrm{SBV}$ functions whose jump set is essentially closed, polyhedral, and preserves the orthogonality to $�N$, moreover the functions are smooth away from their jump set.

Interpolation inequalities for $�C^m$ functions allow to bound derivatives of intermediate order by bounds for the derivatives of order 0 and $�m$. We review various interpolation inequalities for $�L^p$-norms ($��1�\le �p�\le �\infty �$) in arbitrary finite dimensions. They allow us to study ultradifferentiable regularity by lacunary estimates in a comprehensive way, striving for minimal assumptions on the weights.

For finitely generated torsion-free nilpotent groups, the associated Mal'cev Lie algebra of the group is used frequently when studying the $�R_{\infty }$-property. Two such groups have isomorphic Mal'cev Lie algebras if and only if they are abstractly commensurable. We show that the $�R_{\infty }$-property is not invariant under abstract commensurability within the class of finitely generated torsion-free nilpotent groups by providing counterexamples within a class of 2-step nilpotent groups associated to edge-weighted graphs. These groups are abstractly commensurable to 2-step nilpotent quotients of right-angled Artin groups.

In this paper, the authors establish the three-parameter Triebel–Lizorkin spaces and characterize these spaces as the intersection of two flag Triebel–Lizorkin spaces by applying the discrete Littlewood–Paley–Stein analysis. Moreover, they obtain the boundedness of product singular integral operators on the three-parameter Triebel–Lizorkin spaces.