Related papers: An integrability result for $L^p$-vectorfields in …

For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\Om \subset \R^m$ satisfies formally the equation $-\Delta_p =1$ in $\Om$ and $|\nabla u|^{p-2}…

We establish the existence and uniqueness of the solution to the Dirichlet problem for the variable exponent $p$-Laplacian on a bounded, smooth domain $\Omega \subset {\mathbb R}^n$, where the boundary datum belongs to $W^{1,p}(\Omega)$.…

Let $D$ be a nonnegative integer and ${\mathbf{\Theta}}\subset S^1$ be a lacunary set of directions of order $D$. We show that the $L^p$ norms, $1<p<\infty$, of the maximal directional Hilbert transform in the plane $$ H_{{\mathbf{\Theta}}}…

Differential $p$-forms and $q$-vector fields with constant coefficients are studied. Differential $p$-forms of degrees $p=1,2,n-1,n$ with constant coefficients on a smooth $n$-dimensional manifold $M$ are characterized. In the contravariant…

It is well-known that for a harmonic function $u$ defined on the unit ball of the $d$-dimensional Euclidean space, $d\geq 2$, the tangential and normal component of the gradient $\nabla u$ on the sphere are comparable by means of the…

We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form $\Gamma(t)=(t,\varphi(t)), t\in\R{n}$. When $\varphi$ satisfies suitable curvature and monotonicity conditions, we prove…

Let $\Omega\subset \mathbb{R}^n$ be a bounded $C^1$ domain and $p>1$. For $\alpha>0$, define the quantity \[ \Lambda(\alpha)=\inf_{u\in W^{1,p}(\Omega),\, u\not\equiv 0} \Big(\int_\Omega |\nabla u|^p\,\mathrm{d}x - \alpha…

We prove in particular that for any sufficiently large prime $p$ there is $1\le a<p$ such that all partial quotients of $a/p$ are bounded by $O(\log p/\log \log p)$. For composite denominators a similar result is obtained. This improves the…

We consider multilinear averages in ergodic theory and harmonic analysis and prove their divergence in some range of $L^p$ spaces, with $p$ close enough to 1. We also prove that the trilinear Hilbert transform is unbounded in a similar…

We study higher regularity for weak solutions of the $p$-Laplace equation $-\Delta_p u = f$ in a domain $\Omega \subset \mathbb{R}^n$ for $p$ sufficiently close to 2. For $m \ge 3$, assuming that $f$ satisfies suitable Sobolev and H\"older…

We prove global, or space-time weighted, versions of the Gagliardo-Nirenberg interpolation inequality, with $L^p$ ($p < \infty$) endpoint, adapted to a hyperboloidal foliation. The corresponding versions with $L^\infty$ endpoint was first…

We show that for any regular bounded domain $\Omega\subseteq \mathbb R^n$, $n=2,3$, there exist infinitely many global diffeomorphisms equal to the identity on $\partial \Omega$ which solve the Eikonal equation. We also provide explicit…

We show weak* in measures on $\bar\O$/ weak-$L^1$ sequential continuity of $u\mapsto f(x,\nabla u):W^{1,p}(\O;\R^m)\to L^1(\O)$, where $f(x,\cdot)$ is a null Lagrangian for $x\in\O$, it is a null Lagrangian at the boundary for…

Let $S$ be a closed Riemann surface of genus $g \geq 2$ and $\varphi$ be a conformal automorphism of $S$ of prime order $p$ such that $S/\langle \varphi \rangle$ has genus zero. Let ${\mathbb K} \leq {\mathbb C}$ be a field of definition of…

In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if $p\colon\overline{\Omega}\times \overline{\Omega}\to (1,\infty)$ and $q:\partial \Omega \rightarrow (1,\infty)$ are…

The model of kappa-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper we present new results concerning different sets of derivatives on the coordinate algebra of…

This paper studies the asymptotic behavior of the flux and circulation of a subclass of random fields within the family of 2-dimensional vector ambit fields. We show that, under proper normalization, the flux and the circulation converge…

We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an $\ell^p$ condition and a generalized bounded variation condition. This latter condition requires that a sequence can be…

We establish the $L^p$-boundedness of the local covariant Riesz transform for differential forms on manifold $M$ with bounded $\|Rm\|$. Let $\Delta_j$ be the Hodge Laplace operator on $j$-forms. For any $p \in (1, \infty)$ and…

We study the $\Gamma$-convergence of a family of non-local, non-convex functionals in $L^p(I)$ for $p \ge 1$, where $I$ is an open interval. We show that the limit is a multiple of the $W^{1, p}(I)$ semi-norm to the power $p$ when $p>1$…