Related papers: Higher Order Riesz Transforms for Laguerre Expansi…

In this paper, the mean value formula depends on the Bessel generalized shift operator corresponding to the solutions of the boundary value problem related to the Bessel operator are studied. In addition to, Riesz Bessel transforms related…

We study the boundedness on $L^p$ of the Riesz transform $\nabla L^{-1/2}$, where $L$ is one of several operators defined on $\R$ or $\R_+$, endowed with the measure $r^{d-1} dr$, $d > 1$, where $dr$ is Lebesgue measure. For integer $d$,…

In this paper we study Lp-boundedness properties for area Littlewood-Paley functions associated with heat semigroups for Hermite and Laguerre operators

We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 3/4 for fourth order Schr\"odinger operators in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of…

This is an expository paper on the characterization of the even (or odd) smooth homogeneous convolution Calder\'on-Zygmund operators in R^n such that the maximal singular integral can be controlled in the L^2 norm by the singular integral.…

Given a bounded Lipschitz domain $D\subset \mathbb{R}^d,$ a convolution Calder\'{o}n-Zygmund operator $T$ and a growth function $\omega(x)$ of type $n$, we study what conditions on the boundary of the domain are sufficient for boundedness…

We prove that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$ and a maximally modulated Calder\'on-Zygmund singular integral operator…

The paper deals with the Sturm-Liouville operator $$ Ly=-y^{\prime\prime}+q(x)y,\qquad x\in\lbrack0,1], $$ generated in the space $L_{2}=L_{2}[0,1]$ by periodic or antiperiodic boundary conditions. Several theorems on Riesz basis property…

For a fixed d-tuple $\alpha=(\alpha_1,...,\alpha_d)\in(-1,\infty)^d$, consider the product space $\mathbb{R}_+^d:=(0,\infty)^d$ equipped with Euclidean distance $\arrowvert \cdot \arrowvert$ and the measure…

We consider a regular indefinite Sturm-Liouville eigenvalue problem \{$-f" + q f = \lambda r f$} on $[a,b]$ subject to general self-adjoint boundary conditions and with a weight function $r$ which changes its sign at finitely many,…

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,…

We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter H\"ormander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots +…

We study the $L^{p},$ $1\leqslant p\leqslant \infty,$ boundedness for Riesz transforms of the form $V^{a}(-\frac{1}{2}\Delta+V)^{-a},$ where $a>0$ and $V$ is a non-negative potential. We prove that $V^{a}(-\frac{1}{2}\Delta+V)^{-a}$ is…

Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian and consider the natural weighted Laplacian $\mathcal{A}$ on $L^2(\gamma_{-1})$. In this paper, we prove boundedness and…

Let $w$ be a Muckenhoupt $A_2(\mathbb{R}^n)$ weight and $L_w:=-w^{-1}\mathop\mathrm{div}(A\nabla)$ the degenerate elliptic operator on the Euclidean space $\mathbb{R}^n$. In this article, the authors establish the Riesz transform…

The paper concerns the magnetic Schr\"odinger operator on $R^n$. Under certain conditions, given in terms of the reverse H\"older inequality on the magnetic field and the electric potential, we prove some $L^p$ estimates on the Riesz…

This article focuses on $L^p$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. We introduce four critical…

In this article, we study $m$-order logarithmic Laplacian $\mathcal{L}_m$, which is a singular integro-differential operator with symbol $\big(2\ln |\cdot|\big)^m$ by the Fourier transform. With help of these logarithmic Laplacians, we…

We prove the $L^p$-boundedness, for $p \in (1,\infty)$, of the first order Riesz transform associated to the flow Laplacian on a homogeneous tree with the canonical flow measure. This result was previously proved to hold for $p \in (1,2]$…

We present a fundamentally new proof of the dimensionless Lp boundedness of the Bakry Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion than previous…