Related papers: Preserving closedness of operators under summation

We characterise regular boundary points of the parabolic $p$-Laplacian in terms of a family of barriers, both when $p>2$ and $1<p<2$. Due to the fact that $p\not=2$, it turns out that one can multiply the $p$-Laplace operator by a positive…

In this paper, we give conditions forcing nilpotent operators (everywhere bounded or closed) to be null. More precisely, it is mainly shown any closed or everywhere defined bounded nilpotent operator with a positive (self-adjoint) real part…

We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…

In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.…

We study the lacunary analogue of the $\delta$-discretised spherical maximal operators introduced by Hickman and Jan\v{c}ar, for $\delta \in (0, 1/2)$, and establish the boundedness on $L^p$ for all $1 < p < \infty$, along with the endpoint…

We completely characterize the boundedness of the area operators from the Bergman spaces $A^p_\alpha(\mathbb{B}_ n)$ to the Lebesgue spaces $L^q(\mathbb{S}_ n)$ for all $0<p,q<\infty$. For the case $n=1$, some partial results were…

In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…

The aim of this article is to establish the $L^p(\mathbb{R}^2)$-boundedness of the variational operator associated with averaging operators defined over finite type curves in the plane. Additionally, we present the necessary conditions for…

This paper is primarily concerned with the problem of maximality for the sum $A+B$ and composition $L^{*}ML$ in non-reflexive Banach space settings under qualifications constraints involving the domains of $A,B,M$. Here $X$, $Y$ are Banach…

A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a…

We study an elliptic differential operator A on a manifold with conic points. Assuming A to be defined on the smooth functions supported away from the singularities, we first address the question of possible closed extensions of A to L^p…

Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T is…

In this paper we study optimal control problems with either fractional or regional fractional $p$-Laplace equation, of order $s$ and $p\in [2,\infty)$, as constraints over a bounded open set with Lipschitz continuous boundary. The control,…

In recent articles it was proved that when $\mu$ is a finite, radial measure in $\real^n$ with a bounded, radially decreasing density, the $L^p(\mu)$ norm of the associated maximal operator $M_\mu$ grows to infinity with the dimension for a…

In this survey, we collect recent progress in the understanding of $L^{p}$ bounds for bilinear spherical averages and some associated maximal functions like the bilinear spherical maximal function and its lacunary counterpart. We describe…

We consider the action of finitely truncated singular integral operators on functions taking values in a Banach space. Such operators are bounded for any Banach space, but we show a quantitative improvement over the trivial bound in any…

We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…

In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the…

We investigate the construction and performance of summation-by-parts (SBP) operators, which offer a powerful framework for the systematic development of structure-preserving numerical discretizations of partial differential equations.…

We study the two membranes problem for different operators, possibly nonlocal. We prove a general result about the H\"older continuity of the solutions and we develop a viscosity solution approach to this problem. Then we obtain…