相关论文: On plate decompositions of cone multipliers

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…

Recently Wolff obtained a sharp $L^2$ bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of ``elliptic surfaces'' such as paraboloids and spheres.…

We extend Wolff's "local smoothing" inequality to a wider class of not necessarily conical hypersurfaces of codimension 1. This class includes surfaces with nonvanishing curvature, as well as certain surfaces with more than one flat…

We investigate connections between radial Fourier multipliers on $R^d$ and certain conical Fourier multipliers on $R^{d+1}$. As an application we obtain a new weak type endpoint bound for the Bochner-Riesz multipliers associated to the…

This work is devoted to studying the boundedness on Lebesgue spaces of bilinear multipliers on $\R$ whose symbol is narrowly supported around a curve (in the frequency plane). We are looking for the optimal decay rate (depending on the…

Recently Wolff obtained a nearly sharp $L^2$ bilinear restriction theorem for bounded subsets of the cone in general dimension. We obtain the endpoint of Wolff's estimate and generalize to the case when one of the subsets is large. As a…

It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in…

We revisit the Ou-Wang's approach to the cone restriction problem via polynomial partitioning. By recasting their inductive scheme as a recursive algorithm and incorporating the nested polynomial Wolff axioms, we obtain improved bounds for…

We give characterizations of radial Fourier multipliers as acting on radial L^p-functions, 1<p<2d/(d+1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding…

An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension $d \geq 4$. The proof uses a weighted version of the broad restriction inequality, a narrow decoupling inequality…

In this article we revisit some classical conjectures in harmonic analysis in the setting of mixed norm spaces $L^p_{rad} L^2_{ang} (\mathbb{R}^n)$. We produce sharp bounds for the restriction of the Fourier transform to compact…

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…

For $p\ge 2$, and $\lambda>\max\{n|\tfrac 1p-\tfrac 12|-\tfrac12, 0\}$, we prove the pointwise convergence of cone multipliers, i.e. $$ \lim_{t\to\infty}T_t^\lambda(f)\to f \text{ a.e.},$$ where $f\in L^p(\mathbb R^n)$ satisfies $supp\…

A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $L^p-L^q$ restriction…

In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on $L^p(\mathbb{R}^d)$. Noteworthy examples satisfying the criterion are multipliers of the Mikhlin type or limited decay which…

The Fourier restriction conjecture is a fundamental problem in harmonic analysis. In this paper, we investigate restriction estimates for degenerate higher codimensional quadratic surfaces and obtain sharp results for some types of…

Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…

In this work, we study Fourier multipliers on noncommutative spaces. In particluar, we show a simple proof of $L^p$-$L^q$ estimate of Fourier multipliers on general noncommutative spaces associated with semi-finite von Neumann algebras.…

The classical cone multipliers are Fourier multiplier operators which localize to narrow $1/R$-neighborhoods of the truncated light cone in frequency space. By composing such convolution operators with suitable translation invariant Fourier…

In this note we study the $L^p-L^q$ boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq q <\infty$. The underlying Fourier analysis is associated…