相关论文: Damping estimates for oscillatory integral operato…

In this manuscript, we provide local $L^q$-estimates for the gradient of solutions of a class of quasilinear equations whose principal part lacks strong monotonicity. These estimates are used to establish uniform large-scale $L^q$-estimates…

We prove a wide range of L^p estimates for a trilinear singular integral operator motivated by dropping one average in Calder\'{o}n's second commutator. For comparison by dropping two averages in Calder\'{o}n's second commutator one faces…

The main objective of the paper is to obtain sharp Lipschitz type estimates for the norm of operator differences $f(L_1,M_1)-f(L_2,M_2)$ for pairs $(L_1,M_1)$ and $(L_2,M_2)$ of commuting maximal dissipative operators. To obtain such…

We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for…

Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly…

We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\'e-type covering lemma…

We deal with a real valued integral operator L of Laplace transformation type acting between Lebesgue spaces on the semi-axis. Sufficient conditions for belonging L to Schatten type classes are obtained. Some upper asymptotic estimates for…

In this paper we establish commmutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in the upper half-space $\mathbb{R}^{n+1}_+:=\{(x,t)\in \mathbb{R}^n \times (0,\infty)\}$, with uniformly…

Traditional measures of smoothness often fail to provide accurate $L_p$-error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified…

In this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of continuity in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative…

In this paper quantitative weighted matrix estimates for vector valued extensions of $L^{r'}$-H\"ormander operators and rough singular integrals are studied. Strong type $(p,p)$ estimates, endpoint estimates, and some new results on…

We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded…

This article presents a new primal-dual weak Galerkin method for second order elliptic equations in non-divergence form. The new method is devised as a constrained $L^p$-optimization problem with constraints that mimic the second order…

In this paper we obtain the non - asymptotic estimations for oscillating integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.

We prove certain $L^p$ Sobolev-type inequalities for twisted differential forms on real (and complex) manifolds for the Laplace operator $\Delta$, the differential operators $d$ and $d^*$, and the operator $\bar\partial$. A key tool to get…

In this paper we consider three types of discrete operators stemming from singular Radon transforms. We first extend an $\ell^p$ result for translation invariant discrete singular Radon transforms to a class of twisted operators including…

We obtain $L^p$ estimates of the maximal Schr\"odinger operator in $\mathbb R^n$ using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estimates.

When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for…

Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…