Related papers: Regularity and continuity of the multilinear stron…

Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of…

The Hardy-Littlewood maximal function $\mathcal{M}$ and the trigonometric function $\sin{x}$ are two central objects in harmonic analysis. We prove that $\mathcal{M}$ characterizes $\sin{x}$ in the following way: let $f \in…

We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition…

Let $\mathsf M$ and $\mathsf M _{\mathsf S}$ respectively denote the Hardy-Littlewood maximal operator with respect to cubes and the strong maximal operator on $\mathbb{R}^n$, and let $w$ be a nonnegative locally integrable function on…

We introduce an $R$-sectoriality perturbation technique for non-commuting operators defined in Bochner spaces. Based on this and on bounded $H^{\infty}$-functional calculus results for the Laplacian on manifolds with conical singularities,…

For each $p>1$ and each positive integer $m$ we give intrinsic characterizations of the restriction of the Sobolev space $W^m_p(R)$ and homogeneous Sobolev space $L^m_p(R)$ to an arbitrary closed subset $E$ of the real line. In particular,…

Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various definitions for more than two decades, it has attracted much less attention than its older…

In this article, we fully characterize the measurable Gaussian processes $(U(x))_{x\in\mathcal{D}}$ whose sample paths lie in the Sobolev space of integer order $W^{m,p}(\mathcal{D}),\ m\in\mathbb{N}_0,\ 1 <p<+\infty$, where $\mathcal{D}$…

In this paper, we prove global-in-time $\dot{\mathrm{H}}^{\alpha,q}$-maximal regularity for a class of injective, but not invertible, sectorial operators on a UMD Banach space X , provided $q\in(1,+\infty) , $\alpha\in(-1+1/q,1/q)$. We also…

We prove an analytic version of the stable graph regularity lemma from \cite{MaSh}, which applies to stable functions $f\colon V\times W\to [0,1]$. Our methods involve continuous model theory and, in particular, results on the structure of…

Let $d\ge 1, \ell\in\Z^d$, $m\in \mathbb Z^+$ and $\theta_i$, $i=1,\dots,m $ are fixed, distinct and nonzero real numbers. We show that the $m$-(sub)linear version below of the Ratnakumar and Shrivastava \cite{RS1} Littlewood-Paley square…

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted…

The aim of this paper is to obtain boundedness conditions for the maximal function Mf and to prove the necessary and sufficient conditions for the fractional maximal oparator Ma in the Lorentz Morrey spaces which are a new class of…

In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity…

The main result of this paper is a proof of the continuity of a family of integral functionals defined on the space of functions of bounded variation with respect to a topology under which smooth functions are dense. These functionals occur…

The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal…

We study mapping properties of the centered Hardy--Littlewood maximal operator $\mathcal{M}$ acting on Lorentz spaces. Given $p \in (1,\infty)$ and a metric measure space $\mathfrak{X}$ we let $\Omega^p_{\rm HL}(\mathfrak{X}) \subset…

Results of P. Sj\"olin and F. Soria on the Schr\"odinger maximal operator with complex-valued time are improved by determining up to the endpoint the sharp $s \geq 0$ for which boundedness from the Sobolev space $H^s(\mathbb{R})$ into…

Repeated idempotent elements are commonly used to characterise iterable behaviours in abstract models of computation. Therefore, given a monoid $M$, it is natural to ask how long a sequence of elements of $M$ needs to be to ensure the…

Let $\mathcal{B}$ denote a collection of open bounded sets in $\mathbb{R}^n$, and define the associated maximal operator $M_{\mathcal{B}}$ by $$ M_{\mathcal{B}}f(x) := \sup_{x \in R \in \mathcal{B}} \frac{1}{|R|}\int_R |f|. $$ The sharp…