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

Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers $(1-|\xi|^2-|\eta|^2)^\delta_+$ and we make some advances in this investigation. We obtain…

We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E_{Delta_{S^{2m-1}}}([0,R)) are uniformly bounded as an operator from H^p(S^{2m-1}) to L^p(S^{2m-1}) for all p --> (1,infinity). We also show that…

For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.

We introduce some new functions spaces to investigate some problems at or beyond endpoint. First, we prove that Bochner-Riesz means $B_R^\lambda$ are bounded from some subspaces of $L^p_{|x|^\alpha}$ to $L^p_{|x|^\alpha}$ for $…

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

The $L^p$-boundedness for $p>2$ of the covariant Riesz transform on differential forms is proved for a class of non-compact weighted Riemannian manifolds under certain curvature and volume growth conditions, which in particular settles a…

This paper comprises two parts. In the first, we study $L^p$ to $L^q$ bounds for spectral multipliers and Bochner-Riesz means with negative index in the general setting of abstract self-adjoint operators. In the second we obtain the uniform…

We show that a bilinear radial Fourier multiplier operator with symbol $\sigma$ is $L^2(\R^n)\times L^2(\R^n) \to L^1(\R^n)$ bounded, $n\in \mathbb N,$ if the function $\sigma$ satisfies the smoothness condition $\sigma(2^j\cdot)\Phi\in…

For $ 0< \lambda < \frac{1}2$, let $ B_{\lambda }$ be the Bochner-Riesz multiplier of index $ \lambda $ on the plane. Associated to this multiplier is the critical index $1 < p_\lambda = \frac{4} {3+2 \lambda } < \frac{4}3$. We prove a…

In this paper, we establish the full $L_p$ boundedness of noncommutative Bochner-Riesz means on two-dimensional quantum tori, which completely resolves an open problem raised in \cite{CXY13} in the sense of the $L_p$ convergence for two…

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…

In this paper, we study the bilinear cone multiplier operator in two dimensions. We establish $L^{p_1}\times L^{p_2}\to L^{p}$ boundedness for a regularized version of this operator over a broad range of exponents satisfying the H\"older…

We consider abstract non-negative self-adjoint operators on $L^2(X)$ which satisfy the finite speed propagation property for the corresponding wave equation. For such operators we introduce a restriction type condition which in the case of…

Let $\Delta = \nabla^* \nabla$ be the distinguished Laplacian on a Damek-Ricci space. We prove the $L^{p}$-boundedness of the vector of first-order Riesz transforms $\nabla \Delta^{-1/2}$ in the full range $p\in(1,\infty)$. The most…

In this paper, we study the $L^{p_1}(G) \times L^{p_2}(G)$ to $L^{p}(G)$ boundedness of the bilinear Bochner-Riesz means associated with the sub-Laplacian on M\'etivier group $G$ under the H\"older's relation $1/p = 1/p_1 + 1/p_2$, $1\leq…

In this paper, we study the boundedness of Bochner-Riesz commutator $$[b, S^{\alpha}(\mathcal{L})](f) = b S^{\alpha}(\mathcal{L})(f) - S^{\alpha}(\mathcal{L})(bf)$$ of a $BMO^{\varrho}(\mathbb{R}^d)$ function $b$ and the Bochner-Riesz…

We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on…

This is a continuation of our previous research about an oscillatory integral operator $T_{\alpha, \beta}$ on compact manifolds $\mathbb{M}$. We prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator $T^{*}_{\alpha,…

We prove the $L^p$-boundedness for all $p \in (1,\infty)$ of the first-order Riesz transforms $X_j \mathcal{L}^{-1/2}$ associated with the Laplacian $\mathcal{L} = -\sum_{j=0}^n X_j^2$ on the $ax+b$-group $G = \mathbb{R}^n \rtimes…

We establish the $L^p$-boundedness of the local covariant Riesz transform for differential forms on manifold $M$ with bounded $\|Rm\|$. Let $\Delta_j$ be the Hodge Laplace operator on $j$-forms. For any $p \in (1, \infty)$ and…