Related papers: Holomorphic functional calculus of Hodge-Dirac ope…

Perturbed Hodge-Dirac operators and their holomorphic functional calculi, as investigated in the papers by Axelsson, Keith and the second author, provided insight into the solution of the Kato square-root problem for elliptic operators in…

We prove $R$-bisectoriality and boundedness of the $H^\infty$-functional calculus in $L^p$ for all $1<p<\infty$ for the Hodge-Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry-Emery…

We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a…

The aim of the article is to prove $L^{p}-L^{q}$ off-diagonal estimates and $L^{p}-L^{q}$ boundedness for operators in the functional calculus of certain perturbed first order differential operators of Dirac type for with $p\le q$ in a…

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on…

Let $L$ be a one-to-one operator of type $\omega$ in $L^2(\mathbb{R}^n)$, with $\omega\in[0,\,\pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$…

We derive conditions that ensure the existence of a bounded $H_\infty$-calculus in weighted $L_p$-Sobolev spaces for closed extensions $\underline{A}_T$ of a differential operator $A$ on a conic manifold with boundary, subject to…

We establish an $\mathrm{L}^p$-index theorem for Dolbeault--Dirac operators on compact K\"ahler manifolds with coefficients in a Hermitian holomorphic vector bundle $E$. For every $p \in (1,\infty)$, we prove that the closed…

For an operator generating a group on $L^p$ spaces transference results give bounds on the Phillips functional calculus also known as spectral multiplier estimates. In this paper we consider specific group generators which are abstraction…

This paper concerns Hodge-Dirac operators D = d + $\delta$ acting in L p ($\Omega$, {\lambda}) where $\Omega$ is a bounded open subset of R n satisfying some kind of Lipschitz condition, {\lambda} is the exterior algebra of R n , d is the…

We make some remarks on earlier works on $R-$bisectoriality in $L^p$ of perturbed first order differential operators by Hyt\"onen, McIntosh and Portal. They have shown that this is equivalent to bounded holomorphic functional calculus in…

This note deals with the boundedness of the $H^\infty$ functional calculus of Ritt operators $T$ and associated square function estimates. The purpose is to give a shorter, concise and slightly more general approach towards Le~Merdy's…

The boundedness from $H^p \times L^2$ to $L^r$, $1/p+1/2=1/r$, and from $H^p \times L^{\infty}$ to $L^p$ of bilinear pseudo-differential operators is proved under the assumption that their symbols are in the bilinear H\"ormander class…

We develop an $\mathrm{L}^p$-theory for Dolbeault-Dirac operators on compact K\"ahler manifolds with coefficients in a Hermitian holomorphic vector bundle $E$. For each $p \in (1,\infty)$ we consider the closed $\mathrm{L}^p$-realization…

We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in $L_2$ for small complex $L_\infty$ perturbations of a coefficient matrix which is either real symmetric,…

A Ritt operator T : X --> X on Banach space is a power bounded operator such that the sequence of all n(T^{n} -T^{n-1}) is bounded. When X=Lp for some 1<p<\infty, we study the validity of square functions estimates Norm{(\sum_k k |T^{k}(x)…

For any Ritt operator $T$ acting on a noncommutative $L^p$-space, we define the notion of \textit{completely} bounded functional calculus $H^\infty(B_\gamma)$ where $B_\gamma$ is a Stolz domain. Moreover, we introduce the `column square…

We study the Stokes operator with Hodge, Navier, and Robin boundary conditions on domains $\Omega\subseteq\mathbb{R}^d$ that are uniformly $C^{2,1}$. Starting with the Hodge Laplacian we etablish a bounded H\"ormander functional calculus…

This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…

We study certain differential operators of the form AD arising from a first-order approach to the Kato square root problem. We show that if such operators are R-bisectorial in L^p, they remain R-bisectorial in L^q for all q close to p. In…