Related papers: Smoothing theorems for Radon transforms over hyper…
In this paper we consider $L^p$ boundedness of some commutators of Riesz transforms associated to Schr\"{o}dinger operator $P=-\Delta+V(x)$ on $\mathbb{R}^n, n\geq 3$. We assume that $V(x)$ is non-zero, nonnegative, and belongs to $B_q$ for…
In this paper, we study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, we obtain the following results. 1- Let $1\leq q\leq p\leq \infty$. Then a bounded $(L^{1, p}, L^{1,…
This paper establishes a necessary and sufficient condition for $L^p$-boundedness of a class of multilinear functionals which includes both the Brascamp-Lieb inequalities and generalized Radon transforms associated to algebraic incidence…
We study some basic analytic questions related to differential operators on Lie manifolds, which are manifolds whose large scale geometry can be described by a a Lie algebra of vector fields on a compactification. We extend to Lie manifolds…
We show $\ell^p\big(\mathbb Z^d\big)$ boundedness, for $p\in(1, \infty)$, of discrete singular integrals of Radon type with the aid of appropriate square function estimates, which can be thought as a discrete counterpart of the…
We prove $L^p_{comp}\to L^p_{s}$ boundedness for averaging operators associated to a class of curves in the Heisenberg group $\mathbb{H}^1$ via $L^2$ estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities…
Suppose $\lambda_1$ and $\lambda_2$ are infinitely divisible Radon measures on real Banach spaces $E_1$ and $E_2$, respectively and let $T:E_{1} \rightarrow E_{2}$ be a Borel measurable mapping so that $T(\lambda_1) * \rho = \lambda_2 $ for…
We study $L^p$-Sobolev regularity estimate for the restricted X-ray transforms generated by nondegenerate curves. Making use of the inductive strategy in the recent work by the authors, we establish the sharp $L^p$-regularity estimates for…
On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space $\mathcal{D}^{1,p}_0$ into $L^q$ and the summability properties of the distance function. We prove that in the…
In this paper we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results and the…
In this paper we investigate $L^p$ and Sobolev boundedness of a certain class of pseudodifferential operators with non-regular symbols. We employ regularisation methods, namely convolution with a net of mollifiers $(\rho_\eps)_\eps$, and we…
We develop a sharp maximal regularity theory for the resolvent and evolution Stokes equations with no-slip boundary conditions, focusing on bounded domains of low regularity. Our framework covers the full scales of Besov and Sobolev spaces,…
We study the microlocal properties of generalized Radon transforms over a family of quadric hypersurfaces whose centers lie on an orientable hypersurface $S$. The quadric surfaces we consider are level sets of the quadratic form associated…
As it was shown by Shen, the Riesz transforms associated to the Schr\"odinger operator $L=-\Delta + V$ are not bounded on $L^p(\mathbb{R}^d)$-spaces for all $p, 1<p<\infty$, under the only assumption that the potential satisfies a reverse…
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from $\ell^p$ to $\ell^q$…
We study the interrelation between the limit $L_p(\Omega)$-Sobolev regularity $\overline{s}_p$ of (classes of) functions on bounded Lipschitz domains $\Omega\subseteq\mathbb{R}^d$, $d\geq 2$, and the limit regularity $\overline{\alpha}_p$…
In this paper we consider the so-called crystallographic Radon transform (or crystallographic $X$-ray transform) and totally geodesic Radon transform on the group of rotations SO(3). As we show both of these transforms naturally appear in…
In the setting of a general Borel measure $\mu$ on $R^d$ with the natural ball size condition $$\mu[B(x,r)]\leq Cr^s,$$ we establish the $L^p(\mu)$-$L^q(\mu)$-estimate for the generalized Radon transform…
A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach beyond…
We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…