Related papers: Singular integrals unsuitable for the curvature me…
We consider linear spectral-meromorphic (s-meromorphic) OD operators at the real axis such that all local solutions to the eigenvalue problems are meromorphic for all $\lambda$. By definition, rank one algebro-geometrical operator $L$ admit…
This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadratic forms. Such integral operators naturally arise when…
Recently, Bansah and Sehba studied in [3] the boundedness of a family of Hilbert-type integral operators, where they characterized the $L^{p}-L^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. In this paper, we deal with…
The local $L^2$-mapping property of Fourier integral operators has been established in H\"ormander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global $L^2$-boundedness for a class of operators that appears naturally in many…
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. Properties of the extremal operators, that is, the operators which achieve equality, are investigated. Specifically, a…
We show how to define curvature as a measure using the Gauss-Bonnet Theorem on a family of singular surfaces obtained by gluing together smooth surfaces along boundary curves. We find an explicit formula for the curvature measure as a sum…
We use PDE methods as developed for the Liouville equation to study the existence of conformal metrics with prescribed singularities on surfaces with boundary, the boundary condition being constant geodesic curvature. Our first result shows…
We are concerned with the similarity problem for Cowen-Douglas operator tuples. The unitary equivalence counterpart was already investigated in the 1970's and geometric concepts including vector bundles and curvature appeared in the…
We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…
We prove the existence of a $(d-2)$-dimensional purely unrectifiable set upon which a family of \emph{even} singular integral operators is bounded.
We establish new connections between integral curvature bounds and the Euler characteristic of closed Riemannian manifolds through the perspective of Schr\"odinger-type operators. Central to our approach is the twisted Dirac operator…
We consider the case with boundary of the classical Kazdan-Warner problem in dimension greater or equal than three, i.e. the prescription of scalar and boundary mean curvatures via conformal deformations of the metric. We deal in particular…
In this paper, the fractional integral operator on non-homogeneous metric measure spaces is introduced, which contains the classic fractional integral operator, fractional integral with non-doubling measures and fractional integral with…
We deal with existence, uniqueness, and regularity for solutions of the boundary value problem $$ \begin{cases} {\mathcal L}^s u = \mu &\quad \text{in $\Omega$}, u(x)=0 \quad &\text{on} \ \ \mathbb{R}^N\backslash\Omega, \end{cases} $$ where…
In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under…
Reparameterization invariance, a symmetry of heavy quark effective theory, appears in different forms in the literature. The most commonly cited forms of the reparameterization transformation are shown to induce the same constraints on…
Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…
We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…
We establish weighted norm inequalities for multilinear singular integral operators with rough kernels. Specifically, we consider the multilinear singular integral operator $\mathcal{L}_\Omega$ associated with an integrable function…