Related papers: Weighted wave envelope estimates for the parabola

We show local smoothing estimates in $L^p$-spaces for solutions to the Hermite wave equation. For this purpose, we obtain a parametrix given by a Fourier Integral Operator, which we linearize. This leads us to analyze local smoothing…

We obtain some weighted $L^{p}$-Sobolev estimates with gain on $p$ and the weight for solutions of the $\overline{\partial}$-equation in lineally convex domains of finite type in $\mathbb{C}^{n}$ and apply them to obtain weighted…

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 consider elliptic transmission problems with complex coefficients across an interface. Under proper transmission conditions, that extend known conditions for well-posedness, and sub-ellipticity we derive microlocal and local Carleman…

In this paper, we study both elliptic and parabolic equations in non-divergence form with singular degenerate coefficients. Weighted and mixed-norm $L_p$-estimates and solvability are established under some suitable partially weighted BMO…

Via the new weight $A_{\vec p}^{\theta }(\varphi )$, the authors introduce a new class of multilinear square operators. The boundedness on the weighted Lebesgue space and the weighted Morrey space is obtained, respectively. Our results…

In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…

Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$. By spectral theory, we can define the operator $F(L)$, which is bounded on $L^2(X)$, for any bounded Borel function $F$. In this paper, we study the sharp weighted…

In this paper, we establish a good-$\lz$ inequality with two parameters in the Schr\"odinger settings. As it's applications, we obtain weighted estimates for spectral multipliers and Littlewood-Paley operators and their commutators in the…

In this paper, the authors establish some weighted estimates for the Calder\'on commutator defined by \begin{eqnarray*} &&\mathcal{C}_{m+1,\,A}(a_1,\dots,a_{m};f)(x) &&\quad={\rm…

We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…

This paper investigates weighted mixed-norm estimates for divergence-type parabolic equations on Reifenberg-flat domains with the conormal derivative boundary condition. The leading coefficients are assumed to be merely measurable in the…

We use the polynomial partitioning method of Guth to prove weighted Fourier restriction estimates in $\Bbb R^3$ with exponents $p$ that range between $3$ and $3.25$, depending on the weight. As a corollary to our main theorem, we obtain new…

Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the wave…

We give an algorithm to compute weighted Ehrhart functions of lattice polytopes for polynomial weights using Lagrange interpolation. We show how to compute generating functions of polynomials using those of unit cubes and Eulerian numbers,…

In this paper we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted $L^p$…

In this paper, we characterize the weighted infinitesimal boundedness: for $0<\alpha<n$ and $1<p<\infty$, $$\|V\phi\|_{L^{p}(w)}^{p}\leq\epsilon\|(-\Delta)^{\frac{\alpha}{2}}\phi\|_{L^{p}(w)}^{p}+C(\epsilon)\|\phi\|_{L^{p}(w)}^{p}.$$ In…

We prove weighted $L_{p,q}$-estimates for divergence type higher order elliptic and parabolic systems with irregular coefficients on Reifenberg flat domains. In particular, in the parabolic case the coefficients do not have any regularity…

In this paper, we complete the analysis initiated in [AFV24] establishing some higher order $C^{k+2,\alpha}$ Schauder estimates ($k \in \mathbb{N}$) for a a class of parabolic equations with weights that are degenerate/singular on a…

In this note we show that the weighted $L^{2}$-Sobolev estimates obtained by P. Charpentier, Y. Dupain & M. Mounkaila for the weighted Bergman projection of the Hilbert space $L^{2}\left(\Omega,d\mu_{0}\right)$ where $\Omega$ is a smoothly…