Related papers: Duality of Bochner spaces

We characterize compact metric spaces whose locally flat Lipschitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric characterization to…

The moduli space $\mathcal{M}_d$ of degree $d\geq2$ rational maps can naturally be endowed with a measure $\mu_\mathrm{bif}$ detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation…

In this paper, we establish continuous bilinear decompositions that arise in the study of products between elements in martingale Hardy spaces $ H^p\ (0<p\leqslant 1) $ and functions in their dual spaces. Our decompositions are based on…

This paper studies complete non-compact smooth metric measure space $(M^n,g,\mathrm{e}^{-f}\mathrm{d}v)$ with positive first spectrum $\lambda_1(\Delta_f)$ or satisfying a weighted Poincar\'e inequality with weight function $\rho$. We…

In this article we study the family of $BMO^p$ spaces, $p \geq 1$, in the general context of metric measure spaces. We give a characterization theorem that allows to describe all possible relations between these spaces considered as sets of…

In previous work, we defined extended versions of von Neumann dimension for Banach space representations of sofic groups. The main application was a definition of l^{p}-dimension and, using this, a proof that the actions of a countable…

The article considers the Lorentz space $L_{p,\tau}(\mathbb{T}^{m})$, $2\pi$ of periodic functions of many variables and spaces with mixed logarithmic smoothness. Equivalent norms of a space with mixed logarithmic smoothness are found and…

The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space.…

For $\alpha>0$, the Bargmann projection $P_\alpha$ is the orthogonal projection from $L^2(\gamma_\alpha)$ onto the holomorphic subspace $L^2_{hol}(\gamma_\alpha)$, where $\gamma_\alpha$ is the standard Gaussian probability measure on $\C^n$…

Characterizing rectifiability of Radon measures in Euclidean space has led to fundamental contributions to geometric measure theory. Conditions involving existence of principal values of certain singular integrals…

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of $\mathcal{L}_{p}$-spaces. We use…

We generalize the respective ``double recurrence'' results of Bourgain and of the second author, which established for pairs of $L^{\infty}$ functions on a finite measure space the a.e. convergence of the discrete bilinear ergodic averages…

We study model-theoretic stability and independence in Banach lattices of the form $L_p(X,U,\mu)$, where $1 \leq p < \infty$. We characterize non-dividing using concepts from analysis and show that canonical bases exist as tuples of real…

We discuss Lebesgue spaces $\mathcal{L}^p([a,b],E)$ of Lusin measurable vector-valued functions and the corresponding vector spaces $AC_{L^p}([a,b],E)$ of absolutely continuous functions. These can be used to construct Lie groups…

We establish an explicit characterisation of L\'evy measures on both $L^p$-spaces and UMD Banach spaces. In the case of $L^p$-spaces, L\'evy measures are characterised by an integrability condition, which directly generalises the known…

We prove that for all 1 \le p \le \infty, p not 2, the Lp spaces associated to two von Neumann algebras M,N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach-Stone…

We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…

We identify the smooth points of $L^1(\mu,X)$, and provide some necessary and sufficient conditions for left and right symmetry of points with respect to Birkhoff-James orthogonality in $L^p(\mu,X), 1\leq p<\infty$, where $\mu$ is any…

We prove a version of the Lebesgue Differentiation Theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation basis induced by a von Neumann lifting. As a consequence,…

Self-duality plays a very important role in many applications in field theories possessing topological solitons. In general, the self-duality equations are first order partial differential equations such that their solutions satisfy the…