Related papers: Functionals for Multilinear Fractional Embedding

Our aim is to provide a short and self contained synthesis which generalise and unify various related and unrelated works involving what we call Phi-Sobolev functional inequalities. Such inequalities related to Phi-entropies can be seen in…

On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…

A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional…

We propose a functional framework of fractional Sobolev spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We characterize these spaces as real interpolation of natural order intrinic…

Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…

This note contains two simple observations. First, by the weak factorization of product $H^1$ (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier…

We prove geometric upper bounds for the Poincar\'e and Logarithmic Sobolev constants for Brownian motion on manifolds with sticky reflecting boundary diffusion i.e. extended Wentzell-type boundary condition under general curvature…

An integral for a scalar function with respect to a multimeasure $N$ taking its values in a locally convex space is introduced. The definition is independent of the selections of $N$ and is related to a functional version of the…

This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…

Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…

We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We prove continuous embeddings into Lorentz and intrinsic H\"older spaces. We also prove…

Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fisher information in the Boolean Central Limit Theorem and…

We establish boundedness estimates for solutions of generalized porous medium equations of the form $$ \partial_t u+(-\mathfrak{L})[u^m]=0\quad\quad\text{in $\mathbb{R}^N\times(0,T)$}, $$ where $m\geq1$ and $-\mathfrak{L}$ is a linear,…

This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…

We consider solutions to some semilinear elliptic equations on complete noncompact Riemannian manifolds and study their classification as well as the effect of their presence on the underlying manifold. When the Ricci curvature is…

This is the continuation of our previous work [5], where we introduced and studied some nonlinear integral equations on bounded domains that are related to the sharp Hardy-Littlewood-Sobolev inequality. In this paper, we introduce some…

We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…

We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…

In this paper we establish a new class of weighted Hardy-Sobolev type inequalities under mild monotonicity assumptions on the weight function. As a consequence, we derive the corresponding weighted Sobolev and trace-type inequalities. These…

In this paper we characterize the trace spaces of a class of weighted function spaces of intersection type with mixed regularities. To a large extent we can overcome the difficulty of mixed scales by employing a microscopic improvement in…