Related papers: Smoothing theorems for Radon transforms over hyper…

We define variable parameter analogues of the affine arclength measure on curves and prove near-optimal $L^p$-improving estimates for associated multilinear generalized Radon transforms. Some of our results are new even in the convolution…

We study the $L^p$-theory for the Schr\"odinger operator $\mathcal L_a$ with inverse-square potential $a|x|^{-2}$. Our main result describes when $L^p$-based Sobolev spaces defined in terms of the operator $(\mathcal L_a)^{s/2}$ agree with…

We show how to improve on Theorem 10 in [arXiv:0906.4883], describing when subsets in $W^{1,p}(\mathbb{R}^n)$ are totally bounded subsets of $L^q(\mathbb{R}^n)$ for $p<n$ and $p\le q<p^*$. This improvement was first shown by Dosso, Fofana,…

We survey some $L^{p}$-vanishing results for solutions of Bochner or Simons type equations with refined Kato inequalities, under spectral assumptions on the relevant Schr\"{o}dinger operators. New aspects are included in the picture. In…

This paper establishes the $L^p$ boundedness of wave operators for linear Schr\"odinger equations in $\mathbb{R}^3$ with time-dependent potentials. The approach to the proof is based on new cancellation lemmas. As a typical application…

In this note we prove that the solution of the stationary and the instationary Stokes equations subject to perfect slip boundary conditions on a 2D wedge domain admits optimal regularity in the $L^p$-setting, i.p. it is $W^{2,p}$ in space.…

Let $M$ be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\RR^n \setminus B(0,R)$ for some $R > 0$, each of which carries the standard metric. Our main result is that the Riesz…

Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and…

We show that every $\mathbb{R}^d$-valued Sobolev path with regularity $\alpha$ and integrability $p$ can be lifted to a Sobolev rough path provided $\alpha < 1/p<1/3$. The novelty of our approach is its use of ideas underlying Hairer's…

We consider the continuity property in Lebesgue spaces $L^p(\R^m)$ of wave operators $W_\pm$ of scattering theory for Schr\"odinger operator $H=-\lap + V$ on $\R^m$, $|V(x)|\leq C\ax^{-\delta}$ for some $\delta>2$ when $H$ is of exceptional…

We prove various equivalent characterisations of the Hardy space $H^p_{\mathcal{L}}(\mathbb{C}^n)$ for $0<p<1$ associated with the twisted Laplacian $\mathcal{L}$ which generalises the result of [MPR81] for the case $p=1$. Using the atomic…

For each $m\ge 1$ and $p>2$ we characterize bounded simply connected Sobolev $L^m_p$-extension domains $\Omega\subset R^2$. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in $\Omega$. Its proof is based on a…

We prove an $L^{p}$ estimate $$ \|e^{-itL} \varphi(L)f\|_{p}\lesssim (1+|t|)^s\|f\|_p, \qquad t\in \mathbb{R}, \qquad s=n\left|\frac{1}{2}-\frac{1}{p}\right| $$ for the Schr\"odinger group generated by a semibounded, selfadjoint operator…

If one thinks of a Riemannian metric, $g_1$, analogously as the gradient of the corresponding distance function, $d_1$, with respect to a background Riemannian metric, $g_0$, then a natural question arises as to whether a corresponding…

This paper is the second part of a two-paper series, initiated in arXiv:2603.02163 for scalar PDEs on hypersurfaces, and is concerned with the well-posedness and $\mathrm{L}^p$-based Sobolev regularity of vector-valued PDEs of interest in…

In this paper we connect Calder\'on and Zygmund's notion of $L^p$\- -differentiability with some recent characterizations of Sobolev spaces via the asymptotics of non-local functionals due to Bourgain, Brezis, and Mironescu. We show how the…

In this article we give an extention of the L^2-theory of anisotropic singular perturbations for elliptic problems. We study a linear and some nonlinear problems involving L^p data (1<p<2). Convergences in pseudo Sobolev spaces are proved…

This paper comprises two parts. We first investigate a $L^p$ type of limiting absorption principle for Schr\"odinger operators $H=-\Delta+V$, i.e., In $\mathbb{R}^n$ ($n\ge 3$) we prove the $\epsilon-$uniform…

Let $\sigma$ be arc-length measure on $S^1\subset \mathbb R^2$ and $\Theta$ denote rotation by an angle $\theta \in (0, \pi]$. Define a model bilinear generalized Radon transform, $$B_{\theta}(f,g)(x)=\int_{S^1} f(x-y)g(x-\Theta y)\,…

Given a bounded subanalytic submanifold of $\mathbb{R}^n$, possibly admitting singularities within its closure, we study the cohomology of $L^p$ differential forms having an $L^p$ exterior differential (in the sense of currents) and…