Related papers: Weighted estimates for Hodge-Maxwell systems
We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the…
In this paper, we are concerned with possibly degenerate stochastic partial differential equations (SPDEs). An $L^2$-theory is introduced, from which we derive the H\"ormander theorem with an analytical approach. With the method of De…
We give a simpler proof of the a priori estimates obtained in the paper by Duran, Sanmartino and Toschi for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class $A_p$. The argument is a…
In this article, with introducing concepts of variable scalar $\mathcal{A}_{p(\cdot),\infty}$ weights and variable matrix $\mathscr{A}_{p(\cdot),\infty}$ weights, we seek a comprehensive theory of $A_\infty$ weights within the framework of…
We prove the mixed-norm Sobolev estimates for solutions to both divergence and non-divergence form time-dependent Stokes systems with unbounded measurable coefficients having small mean oscillations with respect to the spatial variable in…
This paper studies the Sobolev regularity estimates of weak solutions of a class of singular quasi-linear elliptic problems of the form $u_t - \mbox{div}[\mathbb{A}(x,t,u,\nabla u)]= \mbox{div}[{\mathbf F}]$ with homogeneous Dirichlet…
An equivalent norm in the weighted Bergman space $A^p_\omega$, induced by an $\omega$ in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood-Paley inequalities are also…
A global solvability result of the Cauchy problem of the two-species Vlasov-Maxwell-Landau system near a given global Maxwellian is established by employing an approach different than that of [5]. Compared with that of [5], the minimal…
The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$, and thus, we consider the boundedness of $M$ in the…
We study the $L^2$--cohomology of certain local systems on non-compact arithmetic ball quotients $X=\Gamma \backslash \B_n$, in particular vanishing and non--vanishing results. We also give generalizations to higher dimensional ball…
In this paper we establish weighted $L^{q}$-$L^{p}$-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in…
Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\operatorname{dist}(x,E)^{-\alpha}$, where $E$ is a closed set in $X$ and $\alpha\in\mathbb R$. We establish sharp conditions, based on the Assouad…
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…
In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous background magnetic field. First, the MHD system is…
We investigate the initial-boundary value problem for the Stokes system in the half-space, within the framework of weighted Lebesgue spaces. Introducing a new weight function defined via a product of powers of distances from fixed points,…
In this paper, we prove weighted $L^p$ estimates for the canonical solutions on product domains. As an application, we show that if $p\in [4, \infty)$, the $\bar\partial$ equation on the Hartogs triangle with $L^p$ data admits $L^p$…
We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result…
Our aim in this paper is to characterize local Muckenhoupt weighted Lebesgue spaces with variable exponent by compactly supported smooth wavelets. We also investigate necessary and sufficient conditions for the corresponding modular…
We present a formula for the interpolation of matrix weighted spaces of vector valued functions via interpolation functors. We apply our formula to the particular case of interpolation of matrix weighted $L^p$ spaces by the real and complex…
We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain's Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First,…