Related papers: Stockwell-Like Frames for Sobolev Spaces

Sobolev embeddings, of arbitrary order, are considered into function spaces on domains of $\mathbb R^n$ endowed with measures whose decay on balls is dominated by a power $d$ of their radius. Norms in arbitrary rearrangement-invariant…

We consider Hardy operators on the half-space, that is, ordinary and fractional Schr\"odinger operators with potentials given by the appropriate power of the distance to the boundary. We show that the scales of homogeneous Sobolev spaces…

We study the fractional Laplacian and the homogeneous Sobolev spaces on R^d , by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit…

Given a Sobolev homeomorphism $f\in W^{2,1}$ in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of $\epsilon$ measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms…

This paper considers a new version of fractional Sobolev spaces $\widetilde{\mathcal{W}}_{\mathcal{U}}^{\beta,p}(\mathbb{C}^{n})$ defined using the concept of tempered ultradistributions with respect to the spaces of ultradifferentiable…

This monograph is an expanded version of the preprint arXiv:1402.1716 or hal-00943396v1.It is devoted to the dynamics on Sobolev spaces of the cubic Szeg{\"o} equation on the circle ${\mathbb S} ^1$,$$ i\partial \_t u=\Pi (\vert u\vert…

Recently, with the progress of science and the characteristic properties that distinguish the Slepian system called Prolate spheroidal wave functions from the others orthonormal systems, it became clear its important contributions in…

Let $\Gamma$ be a graph. Under suitable geometric assumptions on $\Gamma$, we give several equivalent characterizations of Sobolev and Hardy-Sobolev spaces on $\Gamma$, in terms of maximal functionals, Haj{\l} asz type functionals or atomic…

For every $0<s\leq 1$ we construct $s$-dimensional Salem measures in the unit interval that do not admit any Fourier frame. Our examples are generic for each $s$, including all existing types of Salem measures in the literature: random…

We study the behavior of Haar coefficients in Besov and Triebel-Lizorkin spaces on $\mathbb{R}$, for a parameter range in which the Haar system is not an unconditional basis. First, we obtain a range of parameters, extending up to…

We simplify and complete the construction of fully $O(D)$-equivariant fuzzy spheres $S^d_L$, for all dimensions $d\equiv D-1$, initiated in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423]. This is based on imposing a suitable energy…

We construct smooth localized orthonormal bases compatible with homogeneous mixed-norm Triebel-Lizorkin spaces in an anisotropic setting on $\bR^d$. The construction is based on tensor products of so-called univariate brushlet functions…

We obtain polynomial bounds on the growth in time of Sobolev norm of solutions to the cubic defocusing nonlinear Schrodinger equation on two dimensional product space. We also give the angular improved bilinear Strichartz estimates for…

The spectral analysis of operators in heterogeneous and aging media typically requires a functional framework that extends beyond the standard Hilbertian setting. In this paper, we establish a rigorous distributional theory for a class of…

We introduce a new family of refined Sobolev-Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a Burkholder type inequality in a dual norm. The theory we…

In this paper, we study the sequence of orthogonal polynomials $\{S_n\}_{n=0}^{\infty}$ with respect to the Sobolev-type inner product $$\langle f,g \rangle= \int_{-1}^{1} f(x) g(x) \,d\mu(x) +\sum_{j=1}^{N} \eta_{j} \,f^{(d_j)}(c_{j})…

We collect and extend results on the limit of $\sigma^{1-k}(1-\sigma)^k |v|_{l+\sigma,p,\Omega}^p$ as $\sigma$ tends to $0^+$ or $1^-$, where $\Omega$ is $\mathbb{R}^n$ or a smooth bounded domain, $k$ is 0 or 1, $l$ is a nonnegative…

In this paper we prove the Sobolev embeddings for Herz-type Triebel-Lizorkin spaces, \begin{equation*} \dot{K}_{q}^{\alpha_{2},r}F_{\theta }^{s_{2}}\hookrightarrow \dot{K}%_{s}^{\alpha_{1},p}F_{\beta }^{s_{1}} \end{equation*} where the…

A pair of dual frames with almost exponentially localized elements (needlets) are constructed on $\RR_+^d$ based on Laguerre functions. It is shown that the Triebel-Lizorkin and Besov spaces induced by Laguerre expansions can be…

We introduce a scale of anisotropic Sobolev spaces defined through a three-parameter family of Fourier multipliers and study their functional analytic properties. These spaces arise naturally in PDE when studying traveling wave solutions,…