Related papers: On isomorphically polyhedral $\mathcal L_\infty$-s…

We prove that: 1. If a Hausdorff M-space is a continuous closed image of a submetrizable space, then it is metrizable. 2. A dense-in-itself open-closed image of a submetrizable space is submetrizable if and only if it is functionally…

In this paper we study the isometric rigidity of certain classes of metric spaces with respect to the $p$-Wasserstein space. We prove that spaces that split a separable Hilbert space are not isometrically rigid with respect to…

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…

Jae-Suk Park and the second-named author introduce the deformation problem of coisotropic submanifolds of a symplectic manifold as the study of Mauer-Cartan moduli problem of an $L_\infty$ algebra attached to the foliation de-Rham complex…

We show that on certain diffeological spaces there exist linear derivations that satisfy the Leibniz rule but are not smooth with respect to the given diffeology. This reveals that the notion of tangent space defined via all such…

We show that the Hilbert space is coarsely embeddable into any $\ell_p$ for $1\le p<\infty$. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space.

This is an exposition of the known techniques for constructing $\Cal L_p$-spaces for $p\in (1,\infty)\setminus \{2\}$, including some unpublished work of Alspach. Isomorphic and complemented embedding relations between these spaces are also…

We describe the isometry group of $L^2(\Omega, M)$ for Riemannian manifolds $M$ of dimension at least two with irreducible universal cover. We establish a rigidity result for the isometries of these spaces: any isometry arises from an…

In this article we construct examples of L-indistinguishable overconvergent eigenforms for an inner form of SL(2).

We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…

We consider the Hardy-Littlewood-Sobolev inequality on mixed-norm Lebesgue spaces. We give a complete characterization of indices $\vec p$ and $\vec q$ such that the Riesz potential is bounded from $L^{\vec p}$ to $L^{\vec q}$, including…

Let $X$ be any subanalytic compact pseudomanifold. We show a De Rham theorem for $L^\infty$ forms. We prove that the cohomology of $L^\infty$ forms is isomorphic to intersection cohomology in the maximal perversity.

In this article, we consider a higher-order elliptic equation with nonsmooth coefficients with respect to Orlicz spaces on the domain $\Omega\subset\mathbb{R}^{n}$. The separable subspace of this space is distinguished in which infinitely…

Supplementing and expanding classical results, for compact spaces $K$ and $L$, $L$ metric, and their Banach spaces $\mathcal{C}(L)$ and $\mathcal{C}(K)$ of continuous real-valued functions, we provide several characterizations of the…

We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on $\R^d$. This time we study characterizations of these subspaces by differences.

We improve the known results about the complexity of the relation of isomorphism between separable Banach spaces up to Borel reducibility, and we achieve this using the classical spaces $c_0$, $\ell_p$ and $L_p$, $1 \leq p <2$. More…

Parameter-ellipticity with respect to a closed subsector of the complex plane for pseudodifferential Douglis-Nirenberg systems is discussed and shown to imply the existence of a bounded H_\infty-calculus in suitable scales of Sobolev,…

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…

We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…

In this paper we consider the problem of characterization of topological spaces that embed into countably compact Hausdorff spaces. We study the separation axioms of subspaces of countably compact Hausdorff spaces and construct an example…