Related papers: On the Local Regularity of the Hilbert Transform

The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…

In this paper, we study local regularity of the solutions to the Stokes equations near a curved boundary under no-slip or Navier boundary conditions. We extend previous boundary estimates near a flat boundary to that near a curved boundary,…

We analyze smooth nonlinear mappings for Hilbert and Banach spaces that carry small balls to convex sets, provided that the radius of the balls is small enough. Being focused on the study of new and mild sufficient conditions for a…

In this short note we improve some of recent results of Cuckovic and Sahutoglu concerning regularity of the Berezin transform for a class of smooth pseudoconvex domains.

In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…

We are interested in analyzing the preservation of bifurcations in a class of piecewise smooth vector fields with a nonregular switching set under a smoothing process that approximates them by smooth vector fields. We examine cases in which…

This is a survey on rigidity and geometrization results obtained with the help of the discrete Hilbert-Einstein functional, written for the proceedings of the "Discrete Curvature" colloquium in Luminy.

We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the $p$-Laplacian type and in non-divergence form. We provide local H\"older and Lipschitz estimates for the solutions. In the degenerate…

We analyze in this work the regularity properties of the density operator solu- tion to the quantum Liouville equation. As was recently done for the Strichartz inequalities, we extend to systems of orthonormal functions the local smoothing…

In this paper, we deal with sweeping processes on (possibly infinite-dimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the…

We study some properties of smoothing kernels and their local expression as they appear in the construction of Colombeau-type generalized function algebras which are diffeomorphism invariant.

In this paper we establish a number of implications between various qualitative and quantitative versions of the global regularity problem for the Navier-Stokes equations, in the periodic, smooth finite energy, smooth $H^1$, Schwartz, or…

In this paper we study the regularity of the local minima of integral functionals: in particular, not convexity (quasi-convexity, policonvexity or rank one convexity) hypothesis will be made on the density, neither structure hypothesis nor…

Given a strongly local Dirichlet space and $\lambda\geq 0$, we introduce a new notion of $\lambda$--subharmonicity for $L^1_\loc$--functions, which we call \emph{local $\lambda$--shift defectivity}, and which turns out to be equivalent to…

We report on a few interrelations between bi-Hermitian metrics and locally conformally K\"ahler metrics on complex surfaces.

There are investigated problems connected with local and boundary properties of Orlicz--Sobolev classes of finite distortion which are actively studied last time. It is showed that, a locally uniform limit of local homeomorphisms of…

We deal with a class of semilinear nonlocal differential equations in Hilbert spaces which is a general model for some anomalous diffusion equations. By using the theory of integral equations with completely positive kernel together with…

This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…

In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence…

We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…