Related papers: The Weiss conjecture and weak norms

We study the $\varrho$-th order variation seminorm of a general Ornstein--Uhlenbeck semigroup $\left(\mathcal H_t\right)_{t>0}$ in $\mathbb R^n$, taken with respect to $t$. We prove that this seminorm defines an operator of weak type…

These classical inequalities allow one to estimate the number of negative eigenvalues and the sums $S_{\gamma}=\sum |\lambda_i|^{\gamma}$ for a wide class of Schr\"{o}dinger operators. We provide a detailed proof of these inequalities for…

Let E be a Dedekind complete Riesz space with weak unit e, equipped with a conditional expectation operator T. We prove that the spaces Lp(T), with their natural vector-valued norms, are strongly complete, extending the p=2 case of Kuo,…

We obtain, under an additional assumption on the subanalytic abnormal distribution constructed in [4], a proof of the minimal rank Sard conjecture in the analytic category. It establishes that from a given point the set of points accessible…

Let $X$ be a Banach space and $\mu$ a probability measure. A set $K \subseteq L^1(\mu,X)$ is said to be a $\delta\mathcal{S}$-set if it is uniformly integrable and for every $\delta>0$ there is a weakly compact set $W \subseteq X$ such that…

A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{Z}_p \setminus \{0\}$ can be ordered so that all partial sums are distinct. Although this conjecture was recently proved for sufficiently large primes by Pham and…

Recently Blecher and Kashyap have generalized the notion of W* modules over von Neumann algebras to the setting where the operator algebras are \sigma- weakly closed algebras of operators on a Hilbert space. They call these modules weak*…

It is a well-known fact that in a Lipschitz domain \Omega\subset R^n a p-Hardy inequality, with weight d(x,\partial\Omega)^\beta, holds for all u\in C_0^\infty(\Omega) whenever \beta<p-1. We show that actually the same is true under the…

The Feichtinger Conjecture, if true, would have as a corollary that for each set $E\subset \T$ and $\Lambda \subset \Z$, there is a partition $\Lambda_1,...,\Lambda_N$ of $\Z$ such that for each $1\le i \le N$, $\{\exp(2\pi i x\lambda):…

For a class of systems of semi-linear elliptic equations, including \[ -\Delta u_i=f_i(x,u_i) - \beta u_i\sum_{j\neq i}a_{ij}u_j^p,\qquad i=1,\dots,k, \] for $p=2$ (variational-type interaction) or $p = 1$ (symmetric-type interaction), we…

We study $\ell^r$-valued extensions of linear operators defined on Lebesgue spaces with variable exponent. Under some natural (and usual) conditions on the exponents, we characterize $1\leq r\leq \infty$ such that every bounded linear…

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic,…

One of the most beautiful results in the integral representation theory of finite groups is a theorem of A. Weiss that detects a permutation $R$-lattice for the finite $p$-group $G$ in terms of the restriction to a normal subgroup $N$ and…

Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As…

We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing…

We generalize a result of Sury and prove that uniform discreteness of cocompact lattices in higher rank semisimple Lie groups (first conjectured by Margulis) is equivalent to a weak form of Lehmer's conjecture. We include a short survey of…

In this article, we prove a weak type $(p,p)$ maximal inequality, $1<p<\infty$, for weighted averages of a positive Dunford-Schwarz operator $T$ acting on a noncommutative $L_p$-space associated to a semifinite von Neumann algebra…

We prove necessary and sufficient conditions for the weak-$L^p$ boundedness, for $p \in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality enjoyed by the…

We extend the duality principle for the $\Gamma$-convergence of convex lower semicontinuous functions, which was previously established only in separable reflexive Banach spaces, to the broader class of weakly compactly generated (WCG)…

A comprehensive analysis of Sobolev-type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space is offered. A unified approach is proposed, providing one with criteria for their validity in the class of rearrangement-invariant…