Related papers: Monomial convergence on $\ell_r$

We consider a four-dimensional globally hyperbolic spacetime $(M,g)$ conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of…

We show that, on any given finite Borel measure space with the ambient space being a Polish metric space, every Borel real-valued function is almost a bounded, uniformly continuous function in the sense that for every $\varepsilon > 0$…

Let $d$ be a metric on $R^n$ and let $C^{m,(d)}(R^n)$ be the space of $C^m$-function on $R^n$ whose partial derivatives of order $m$ belong to the space $Lip(R^n;d)$. We show that the homogeneous Sobolev space $L^{m+1}_p(R^n),p>n,$ can be…

Let $X$ be a Banach space and $(f_n)_n$ be a bounded sequence in $L^1(X)$. We prove a complemented version of the celebrated Talagrand's dichotomy i.e we show that if $(e_n)_n$ denotes the unit vector basis of $c_0$, there exists a sequence…

For a regular, compact, polynomially convex circled set K in C^2, we construct a sequence of pairs {P_n,Q_n} of homogeneous polynomials in two variables with deg P_n = deg Q_n = n such that the sets K_n: = {(z,w) \in C^2 : |P_n(z,w)| \leq…

We prove that the convergence of the real and imaginary parts of the logarithm of the characteristic polynomial of unitary Brownian motion toward Gaussian free fields on the cylinder, as the matrix dimension goes to infinity, holds in…

Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_2$ on a compact space, Gr\"ochenig in \cite{G} discussed weighted least squares approximation and least squares quadrature. Inspired by this work, for all $1\le p\le\infty$, we…

Consider an $L^1$-continuous functional $\ell$ on the vector space of polynomials of Brownian motion at given times, suppose $\ell $ commutes with the quadratic variation in a natural sense, and consider a finite set of polynomials of…

The Hardy--Littlewood inequality for $m$-homogeneous polynomials on $\ell_{p}$ spaces is valid for $p>m.$ In this note, among other results, we present an optimal version of this inequality for the case $p=m.$ We also show that the optimal…

Over a field $K$ of characteristic $p$, let $Z$ be the incidence variety in $\mathbb{P}^d \times (\mathbb{P}^d)^*$ and let $\mathcal{L}$ be the restriction to $Z$ of the line bundle $\mathcal{O}(-n-d) \boxtimes \mathcal{O}(n)$, where $n =…

Let $p, q \in (0, \infty]$ and $\ell_p^m(\ell_q^n)$ be the mixed-norm sequence space of real matrices $x = (x_{i, j})_{i \leq m, j \leq n}$ endowed with the (quasi-)norm $\Vert x \Vert_{p, q} := \big\Vert \big( \Vert (x_{i, j})_{j \leq n}…

Morrey (function) spaces and, in particular, smoothness spaces of Besov-Morrey or Triebel-Lizorkin-Morrey type enjoyed a lot of interest recently. Here we turn our attention to Morrey sequence spaces $m_{u,p}=m_{u,p}(\mathbb{Z}^d)$,…

With every reduced $E$-Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with zero morphisms $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$-algebras $\Bbbk…

We prove that given a finite set $E$ in a bordered Riemann surface $\mathcal{R}$, there is a continuous map $h\colon \overline{\mathcal{R}}\setminus E\to\mathbb{C}^n$ ($n\geq 2$) such that $h|_{\mathcal{R}\setminus E} \colon…

The maximal Orlicz space such that the mixed logarithmic means of multiple Fourier series for the functions from this space converge in $L_{1}$-norm is found.

We assign a relational structure to any finite algebra in a canonical way, using solution sets of equations, and we prove that this relational structure is polymorphism-homogeneous if and only if the algebra itself is…

Given a convex function $\varphi$ and two hermitian matrices $A$ and $B$, Lewin and Sabin study in [M. Lewin, J. Sabin, {\it A Family of Monotone Quantum Relative Entropies}, Lett. Math. Phys. \textbf{104} (2014), 691-705.] the relative…

Let $\mathcal{X}$ be a space of homogenous type and $\varphi:\ \mathcal{X}\times[0,\infty) \to[0,\infty)$ a growth function such that $\varphi(\cdot,t)$ is a Muckenhoupt weight uniformly in $t$ and $\varphi(x,\cdot)$ an Orlicz function of…

The well-known Bohr--P\'al theorem asserts that for every continuous real-valued function $f$ on the circle $\mathbb T$ there exists a change of variable, i.e., a homeomorphism $h$ of $\mathbb T$ onto itself, such that the Fourier series of…

In this article, we provide a multilinear version of the H\"ormander multiplier theorem with a Lorentz-Sobolev space condition. The work is motivated by the recent result of the first author and Slav\'ikov\'a where an analogous version of…