Related papers: Bochner-Riesz means on a conical singular manifold

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions. We prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying the condition $\lvert 1 / p…

We consider generalized Bochner-Riesz operators associated with planar convex domains. We construct domains which yield improved $L^p$ bounds for the Bochner-Riesz over previous results of Seeger-Ziesler and Cladek. The constructions are…

$ \renewcommand{\subset}{\subseteq} \newcommand{\N}{\mathbb N} $For $p\in [2,\infty)$ the metric $X_p$ inequality with sharp scaling parameter is proven here to hold true in $L_p$. The geometric consequences of this result include the…

Let $\mathcal L$ denote the twisted Laplacian in $\mathbb C^d$. We study almost everywhere convergence of the Bochner--Riesz mean $S^\delta_{t}(\mathcal L) f$ of $f\in L^p(\mathbb C^d)$ as $t\to \infty$, which is an expansion of $f$ in the…

In this article we have investigated $L^{p}$ boundedness of the multilinear maximal Bochner--Riesz means and the corresponding square function. We have exploited the ideas given in the paper "Maximal estimates for bilinear Bochner--Riesz…

Results analogous to those proved by Rubio de Francia are obtained for a class of maximal functions formed by dilations of bilinear multiplier operators of limited decay. We focus our attention to $L^2\times L^2\to L^1$ estimates. We…

We improve the range of indices when the multilinear Bochner-Riesz means converges pointwisely. We obtain this result by establishing the $L^p$ estimates and weighted estimates of $k$-linear maximal Bochner-Riesz operators inductively,…

We establish improved and sharp $L^p$ estimates for the maximal bilinear Bochner-Riesz means in all dimensions $n\geq 1$. This work extends the results proved by Jeong and Lee \cite{JL}. We also recover the known results for the bilinear…

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…

For $1<p<\infty$, we prove the $L^p$-boundedness of the Riesz transform operators on metric measure spaces with Riemannian Ricci curvature bounded from below, without any restriction on their dimension. This large class of spaces include…

We establish various $L^{p}$ estimates for the Schr\"odinger operator $-\Delta+V$ on Riemannian manifolds satisfying the doubling property and a Poincar\'e inequality, where $\Delta $ is the Laplace-Beltrami operator and $V$ belongs to a…

We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L^p-spaces over B, 1 < p < \infty. Under suitable ellipticity…

In this paper, we study the $L^p$-boundedness of Stein's square function $\mathfrak{S}^{\alpha}(\mathcal{L})$ associated with the sub-Laplacian $\mathcal{L}$ on M\'etivier group $G$. A key aspect of our result is that the smoothness…

In [J. Class. Anal., vol. 26 (1) (2025), 63-76], we proved that the discrete Riesz potential $I_{\alpha}$ is a bounded operator $H^p(\mathbb{Z}^n) \to H^q(\mathbb{Z}^n)$ for $\frac{n-1}{n} < p \leq 1$, $\frac{1}{q} = \frac{1}{p} -…

We obtain weak-type $(p, p)$ endpoint bounds for Bochner-Riesz means for the Hermite operator $H=-\Delta +|x|^2$ in ${\mathbb R}^n, n\geq 2$ and for other related operators for $1\leq p\leq 2n/(n+2)$, extending earlier results of Thangavelu…

Let $G$ be a connected, simply connected, compact semisimple Lie group of dimension $n$. It has been shown by Clerc \cite{Clerc1974} that, for any $f\in L^1(G)$, the Bochner-Riesz mean $S_R^\delta(f)$ converges almost everywhere to $f$,…

Let $M$ be a complete non-compact Riemannian manifold satisfying the doubling volume property. Let $\overrightarrow{\Delta}$ be the Hodge-de Rham Laplacian acting on 1-differential forms. According to the Bochner formula,…

We consider the Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p}+V$ on tensor powers $L^p$ of a Hermitian line bundle $L$ on a Riemannian manifold $X$ of bounded geometry under the assumption of non-degeneracy of the curvature…

We study mapping properties of the centered Hardy--Littlewood maximal operator $\mathcal{M}$ acting on Lorentz spaces. Given $p \in (1,\infty)$ and a metric measure space $\mathfrak{X}$ we let $\Omega^p_{\rm HL}(\mathfrak{X}) \subset…

In this article, we investigate the boundedness of the bilinear Bochner-Riesz means $S^{\alpha }$ in the non-Banach triangle case. We improve the corresponding results in [Bern] in two aspects: Our partition of the non-Banach triangle is…