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

In this paper, we give a new approach to the Bochner-Riesz summability. As a result, we show that the Bochner-Riesz operator $\mathbf{S}^\delta, 0<\Re\delta<{1\over 2}$ is bounded on $\mathbf{L}^p(\mathbb{R}^n)$ for ${n-1\over 2n}\leq…

We study $L^p$-boundedness of the Bochner-Riesz means for critical magnetic Schr\"odinger operators $\mathcal{L}_{\bf A}$ in ${\mathbb{R}^2}$, which involve the physcial Aharonov-Bohm potential. We show that for $1\leq p\leq +\infty$ and…

Let $w$ be a Muckenhoupt weight and $WH^p_w(\mathbb R^n)$ be the weighted weak Hardy spaces. In this paper, by using the atomic decomposition of $WH^p_w(\mathbb R^n)$, we will show that the maximal Bochner-Riesz operators $T^\delta_*$ are…

This paper studies the sharp $L^p$-$L^q$ boundedness of the Bochner-Riesz operator $S^{\delta}_{\lambda}(\mathcal{L}_{\mathbf{A}})$ associated with a scaling-critical magnetic Schr\"odinger operator $\mathcal{L}_{\mathbf{A}}$ on…

In this paper, we study the $L^p$-boundedness of the commutator $[b, S_R^\delta(H)](f) = bS_R^\delta(H) f - S_R^\delta(H)(bf)$ of a BMO function $b$ and the Bochner-Riesz means $S_R^\delta(H)$ for Hermite operator $H=-\Delta +|x|^2$ on…

We study the Bochner-Riesz problem for the twisted Laplacian $\mathcal L$ on $\mathbb R^2$. For $p\in [1, \infty]\setminus\{2\}$, it has been conjectured that the Bochner-Riesz means $S_\lambda^\delta(\mathcal L) f$ of order $\delta$…

We investigate $L^p$ boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic type. Assuming the finite speed of propagation for the associated wave operator, from the restriction type estimates we establish the…

For $f\in {\frak S}({\Bbb R}^d)$, we consider the Bochner-Riesz operator ${\frak R}^{\delta}$ of index $\delta>0$ defined by $$\hat {{\frak R}^{\delta}f}(\xi)=(1-|\xi|^2)^{\delta}_+ \hat f (\xi).$$ Then we prove the Bochner-Riesz conjecture…

We prove that the bilinear maximal Bochner-Riesz operator $T_*^\lambda$ is bounded from $L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n)$ to $L^p(\mathbb R^n)$ for appropriate $(p_1,p_2,p)$ when $\lambda>(4n+3)/5$.

We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To…

The Bochner-Riesz multipliers $ B_{\delta }$ on $ \mathbb R ^{n}$ are shown to satisfy a range of sparse bounds, for all $0< \delta < \frac {n-1}2 $. The range of sparse bounds increases to the optimal range, as $ \delta $ increases to the…

We demonstrate the almost everywhere convergence of the planar Bochner-Riesz means for $L^p$ functions in the optimal range when $5/3\leq p\leq 2$. This is achieved by establishing a sharp $L^{5/3}$ estimate for a maximal operator closely…

We consider generalized Bochner-Riesz multipliers of the form $(1-\rho(\xi))_+^{\lambda}$ where $\rho(\xi)$ is the Minkowski functional of a convex domain in $\mathbb{R}^2$, with emphasis on domains for which the usual Carleson-Sj\"{o}lin…

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…

This paper is devoted to the study of $L^{p_1} \times L^{p_2}$ to $L^{p}$ boundedness of the bilinear Bochner-Riesz mean $\mathcal{B}^{\alpha}$ associated with the Grushin operator $\mathcal{L} = -\Delta_{x'} - |x'|^2 \Delta_{x''}$ on…

We study $L^p\times L^q\to L^r$ bounds for the bilinear Bochner-Riesz operator $\mathcal{B}^\alpha$, $\alpha>0$ in $\mathbb{R}^d,$ $d\ge2$, which is defined by \[ {\mathcal B}^{\alpha}(f,g)=\iint_{\mathbb{R}^d\times\mathbb{R}^d} e^{2\pi i…

Let $G=N\rtimes \mathbb{R}$, where $N$ is a Carnot group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$, and their sum is a left-invariant…

In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and unweighted inequalities in…

In this paper, we study the almost everywhere convergence problem for the Bochner--Riesz means $S_t^\delta f$ for $f\in L^p(\mathbb R^d)$ in the subcritical range \[ 0\le \delta < \delta(d,p):=d\Big(\frac12-\frac1p\Big)-\frac12, \qquad…

We consider the Bochner-Riesz means for the Hermite and special Hermite expansions and study their $L^p$ boundedness with the sharp summability index in a local setting. In two dimensions we establish the boundedness on the optimal range of…