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Stability of the Stokes projection on weighted spaces and applications
(American Mathematical Society, 2020-01)
We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\bW^{1,p}_0(\omega,\Omega) \times L^p(\omega,\Omega)$, where the weight belongs to a certain ...
Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
(Birkhauser Boston Inc, 2003-03)
We study boundedness and convergence on Lp(ℝn, dμ) of the projection operators Pj given by MRA structures with non-necessarily compactly supported scaling function. As a consequence, we prove that if w is a locally integrable ...
Schrödinger type singular integrals: weighted estimates for p=1
(Wiley VCH Verlag, 2016-08)
A critical radius function ρ assigns to each x ∈ Rd a positive number in a way that its variation at different points is somehow controlled by a power of the distance between them. This kind of function appears naturally ...
Local fractional and singular integrals on open subsets
(Springer, 2019-07)
For a proper open set $Omega$ immersed in a metric space with the weak homogeneity property, and given a measure $mu$ doubling on a certain family of balls lying ``well inside´´ of $Omega$, we introduce local operators of ...
Proof of an extension of E. Sawyer’s conjecture about weighted mixed weak-type estimates
(Springer Heidelberg, 2019-06)
We show that if v∈ A∞ and u∈ A1, then there is a constant c depending on the A1 constant of u and the A∞ constant of v such that ∥T(fv)v∥L1,∞(uv)≤c‖f‖L1(uv),where T can be the Hardy–Littlewood maximal function or any ...
Weighted inequalities and a.e. convergence for Poisson integrals in light-cones
(Springer, 2006-11)
We show that the Poisson maximal operator for the tube over the light-cone, P*, is bounded in the weighted space L p (w) if and only if the weight w(x) belongs to the Muckenhoupt class A p . We also characterize with a ...
Weighted a priori estimates for elliptic equations
(Polish Academy of Sciences. Institute of Mathematics, 2018-06)
We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class Ap. The argument is a ...
Weighted Lebesgue and $BMO^\gamma $; norm inequalities for the Calderón and Hilbert operators
(Springer, 2019-04)
Necessary and sufficient conditions are given for generalized Calderón and Hilbert operators to be bounded from weighted Lebesgue spaces into suitable weighted BMO and Lipschitz spaces. Moreover, we have obtained new results ...
A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
(Edp Sciences, 2014-02)
In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error ...
A weighted setting for the numerical approximation of the Poisson problem with singular sources
(Society for Industrial and Applied Mathematics, 2020-02)
We consider the approximation of Poisson type problems where the source is given by a singular measure and the domain is a convex polygonal or polyhedral domain. First, we prove the well-posedness of the Poisson problem ...