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On Almost Everywhere Convergence of Bochner-Riesz Means in Higher Dimensions [PDF]

Proceedings of the American Mathematical Society, 1985
In R n {{\mathbf {R}}^n} define ( T λ , r f ) ( ξ ) = f ^
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Spectral Multipliers Ii: Elliptic and Parabolic Operators and Bochner--Riesz Means

Journal of Differential Equations
We establish estimates for the Poisson kernel, the heat kernel, and Bochner--Riesz means defined in terms of $H=-Δ+V$, where $V$ is a possibly large rough real-valued scalar potential and $H$ can have negative eigenvalues. All results are in three space dimensions.
Marius Beceanu, Michael Goldberg
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Bochner-Riesz means on a conical singular manifold

We prove a sharp $L^p$-boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0,\infty) \times \mathbb{S}_σ^1$. The operator $S_λ^δ(Δ_X)$ is bounded on $L^p(X)$ for $1 \leq p \leq \infty$, $p \neq 2$, if and only if $δ> δ_c(p,2) = \max\left\{ 0, 2\left| 1/2 - 1/p \right| - 1/2 \right\}$.
Jia, Qiuye, Zhang, Junyong, Zheng, Jiqiang +2 more
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Bochner–Riesz means for the twisted Laplacian in $\mathbb{R}^{2}$

Revista Matemática Iberoamericana
We study the Bochner–Riesz problem for the twisted Laplacian \mathcal{L} on \mathbb{R}^{2} . For p\in [1, \infty]\setminus\
Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu
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Bilinear Bochner–Riesz means for convex domains and Kakeya maximal function

Mathematische Annalen
In this paper we introduce bilinear Bochner-Riesz means associated with convex domains in the plane $\mathbb R^2$ and study their $L^p-$boundedness properties for a wide range of exponents. One of the important aspects of our proof involves the use of bilinear Kakeya maximal function in the context of bilinear Bochner-Riesz problem.
Ankit Bhojak +2 more
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Almost everywhere convergence of Bochner–Riesz means for the twisted Laplacian

Transactions of the American Mathematical Society
Let L \mathcal L denote the twisted Laplacian in C d \mathbb {C}^d . We study almost everywhere convergence of the Bochner–Riesz mean S t δ ( L ) f S^\delta
Jeong, Eunhee, Lee, Sanghyuk, Ryu, Jaehyeon +2 more
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Complete positivity and distance-avoiding sets. [PDF]

Math Program, 2022
DeCorte E, Filho FMO, Vallentin F.
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On pointwise convergence of multilinear Bochner-Riesz means

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, which is new when $p<2/k$ in higher dimensions.
He, Danqing, Li, Kangwei, Zheng, Jiqiang
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Weyl multipliers, Bochner-Riesz means and special Hermite expansions

Arkiv för Matematik, 1991
In this paper special multipliers for the Weyl transform are studied. The Weyl transform $W(f)$ of a function $f$ on $\mathbb{C}^ n$ is a bounded operator on $L^ 2(\mathbb{R}^ n)$ and enjoys many properties of the Fourier transform such as an analogue of the inversion formula and the Plancherel formula.
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On almost everywhere convergence of planar Bochner-Riesz mean

We demonstrate that 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 associated with the Bochner-Riesz multiplier operator. The estimate depends on a novel refined $L^2$ estimate,
Li, Xiaochun, Wu, Shukun
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