Related papers: A Note on UMD Spaces and Transference in Vector-va…

We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative cases. This allows us to define a motivic Fourier transformation for which we get…

Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of distributions is denoted $\alext$ and is a Banach space under…

Following a recent idea by Ball, we introduce the notion of strongly truncated Riesz space with a suitable spectrum. We prove that, under an extra Archimedean type condition, any strongly truncated Riesz space is isomorphic to a uniformly…

We prove that the class of trilinear multiplier forms with singularity over a one dimensional subspace, including the bilinear Hilbert transform, admit bounded $L^p$-extension to triples of intermediate $\mathrm{UMD}$ spaces. No other…

Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…

A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into $L^\infty(\mathbb R^n)$ is exhibited. Under the same assumption, any function from the relevant fractional-order spaces is shown to…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a H\"older continuous function. The Fourier transform is written as the difference of $\int_{-1}^1…

The 1987 Bourgain-Tzafriri Restricted Invertibility Theorem is one of the most celebrated theorems in analysis. At the time of their work, the authors raised the question of a possible infinite dimensional version of the theorem. In this…

We establish finite-sample error bounds in expectation for transformed Fr\'echet means in Hadamard spaces under minimal assumptions. Transformed Fr\'echet means provide a unifying framework encompassing classical and robust notions of…

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…

The general methods which are powerful for the necessity of bounded commutators are given. As applications, some necessary conditions for bounded commutators are first obtained in certain endpoint cases, and several new characterizations of…

We investigate several boundedness properties of function spaces considered as uniform spaces.

The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…

Let $\vec{p}\in(0,1]^n$ be a $n$-dimensional vector and $A$ a dilation. Let $H_A^{\vec{p}}(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of…

We prove a generalisation of Fernique's theorem which applies to a class of (measurable) functionals on abstract Wiener spaces by using the isoperimetric inequality. Our motivation comes from rough path theory where one deals with iterated…

A Fourier transform from momentum space to twistor space is introduced in twistor string theory, for the first time, for the case where the twistor space is a three-dimensional real projective space, corresponding to ultra-hyperbolic…

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the…

Let $X(\mathbb{R})$ be a separable Banach function space such that the Hardy-Littlewood maximal operator is bounded $X(\mathbb{R})$ and on its associate space $X'(\mathbb{R})$. The algebra $C_X(\dot{\mathbb{R}})$ of continuous Fourier…

We extend the theory of Rubio de Francia extrapolation, including off-diagonal, limited range, and $A_{\infty}$ extrapolation, to the weighted variable Lebesgue spaces. As a consequence we are able to show that a number of different…