Related papers: Covariant Riesz transform on differential forms fo…

We deal with a global Calder\'on-Zygmund type estimate for elliptic obstacle problems of $p$-Laplacian type with measure data. For this paper, we focus on the singular case of growth exponent, i.e. $1<p \le 2-\frac{1}{n}$. In addition, the…

We prove two-sided inequalities for the $L^p$-norm of a pushforward or pullback (with respect to an orientation-preserving diffeomorphism) on oriented volume and Riemannian manifolds. For a function or density on a volume manifold, these…

This article explores weighted $(L^p, L^q)$ inequalities for the Fourier transform in rank one Riemannian symmetric spaces of noncompact type. We establish both necessary and sufficient conditions for these inequalities to hold. To prove…

This paper proves the $L^p$ boundedness of generalized first order Riesz transforms obtained as conditional expectations of martingale transforms \`a la Gundy-Varopoulos for quite general diffusions on manifolds and vector bundles. Several…

In this paper, we show that Hilbert transforms along some curves are bounded on $L^p({\mathbb R}^n;X)$ for some $1<p<\infty$ and some UMD spaces $X$. In particular, we prove that the Hilbert transform along some curves are completely…

This paper present an overview of some of the applications of the martingale inequalities of D.L. Burkholder to $L^p$-bounds for singular integral operators, concentrating on the Hilbert transform, first and second order Riesz transforms,…

The paper concerns the magnetic Schr\"odinger operator on $R^n$. We prove some $L^p$ estimates on the Riesz transforms and we establish some related maximal inequalities. The conditions that we arrive at, are essentially based on the…

We study the problem of an appropriate choice of derivatives associated with discrete Fourier-Bessel expansions. We introduce a new so-called essential measure Fourier-Bessel setting, where the relevant derivative is simply the ordinary…

In this work we obtain weighted $L^p$, $1<p<\infty$, and weak $L\log L$ estimates for the commutator of the Riesz transforms associated to a Schr\"odinger operator $-\lap+V$, where $V$ satisfies some reverse H\"older inequality. The classes…

We prove variation and oscillation $L^p$-inequalities associated with fractional derivatives of certain semigroups of operators and with the family of truncations of Riesz transforms in the inverse Gaussian setting. We also study these…

In this paper, for general plane curves $\gamma$ satisfying some suitable smoothness and curvature conditions, we obtain the single annulus $L^p(\mathbb{R}^2)$-boundedness of the Hilbert transforms $H^\infty_{U,\gamma}$ along the variable…

Let $\nu=(\nu_1,\ldots,\nu_n)\in (-1,\vc)^n$, $n\ge 1$, and let $\mathcal{L}_\nu$ be a self-adjoint extension of the differential operator \[ L_\nu := \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 + \frac{1}{x_i^2}(\nu_i^2 -…

We consider the Riesz transforms of arbitrary order associated with the twisted Laplacian with drift on $\mathbb{C}^n$ and study their strong-type $(p, p)$, $1<p<\infty$, and weak-type $(1, 1)$ boundedness.

We prove explicit $L^p$ bounds for second order Riesz transforms of the sub-Laplacian in the Lie groups $\mathbb H$, $\mathbb{SU}(2)$ and $\mathbb{SL}(2)$

This paper is a survey of some recent results on the validity and the failure of global $W^{2,p}$ regularity properties of smooth solutions of the Poisson equation $\Delta u = f$ on a complete Riemannian manifold $(M,g)$. We review…

In this paper we prove sharp multipolar Hardy-type inequalities in the Riemannian $L^p-$setting for $p\geq 2$ using the method of super-solutions and fundamental results from comparison theory on manifolds, thus generalizing previous…

Let $L$ be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with $L$, such as the heat semigroup and Riesz transform, are not, in general, of…

We give sufficient conditions on the exponent $p: \mathbb R^d\rightarrow [1,\infty)$ for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue spaces $L^{p(\cdot)}(\mathbb R^d, \gamma_d)$, as well as of the new…

We characterize the weights for the Stieltjes transform and the Calder\'on operator to be bounded on the weighted variable Lebesgue spaces $L_w^{p(\cdot)}(0,\infty)$, assuming that the exponent function $p(\cdot)$ is log-H\"older continuous…

In this paper we study higher order Riesz transforms associated with the inverse Gaussian measure given by $\pi ^{n/2}e^{|x|^2}dx$ on $\mathbb{R}^n$. We establish $L^p(\mathbb{R}^n,e^{|x|^2}dx)$-boundedness properties and obtain…