Projected-shear nite element methods for periodic Reissner-Mindlin plate model are analyzed for rectangular meshes. A projection operator is applied to the shear stress term in the bilinear form. Optimal error estimates in the L 2-norm, H 1-norm, and the energy norm for both displacement and rotations are established and gradient superconvergence along the Gauss lines is justiied in some weak s...

We find the sharp range for boundedness of discrete bilinear spherical maximal function dimensions $d \geq 5$. That is, we show that this operator is bounded on $l^{p}(\mathbb{Z}^d)\times l^{q}(\mathbb{Z}^d) \to l^{r}(\mathbb{Z}^d)$ $\frac{1}{p} + \frac{1}{q} \frac{1}{r}$ and $r>\frac{d}{2d-2}$ sharp. Our approach mirrors used by Jeong Lee in continuous setting. For $d=3,4$, our previous work, ...

This paper proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilber...

We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal L p (S 2) → L q (RS 2) estimates for the Fourier extension operator on large spheres in R 3 , which are uniform in the ra...

We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal L(S) → L(RS) estimates for the Fourier extension operator on large spheres in R, which are uniform in the radius R. Two a...

An important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for sharp L results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones, averages over finite type curves in R and associated maximal functions. We observe that the range of p in Wolff’s inequality, for t...

We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal L(S) → L(RS) estimates for the Fourier extension operator on large spheres in R, which are uniform in the radius R. Two a...

Let $\mathbb{H}$ be a $(d-1)$-dimensional hyperbolic paraboloid in $\mathbb{R}^d$ and let $Ef$ the Fourier extension operator associated to $\mathbb{H}$, with $f$ supported $B^{d-1}(0,2)$. We prove that $\lVert Ef \rVert\_{L^p (B(0,R))} \leq C\_{\varepsilon}R^{\varepsilon}\lVert f \rVert\_{L^p}$ for all $p \geq 2(d+2)/d$ whenever $d/2\geq m + 1$, where $m$ is minimum between number of positive ...