We prove some uniform in $ε$ a priori estimates for solutions of the equation $$(\nabla-iA)^2u-V(x)u+(λ\pm iε)u=f, λ\geq0, ε\neq0.$$ The estimates are obtained in terms of Morrey-Campanato norms, and can be used to prove absence of zero-resonances, in a suitable sense, for electromagnetic Hamiltonians. Precise conditions on the size of the \textit{trapping component} of the magnetic field and the non repulsive component of the electric field are given.
Interpolation inequalities between Sobolev and Morrey-Campanato spaces: A common gateway to concentration-compactness and Gagliardo-Nirenberg interpolation inequalities
A characterization of rough fractional type integral operators and Campanato estimates for their commutators on the variable exponent vanishing generalized Morrey spaces
Parabolic sublinear operators with rough kernel generated by parabolic Calderón-Zygmund operators and parabolic local Campanato space estimates for their commutators on the parabolic generalized local Morrey spaces
Strichartz and smoothing estimates in weighted $L^2$ spaces and their applications
本文的主要目的是回答J.A. J. M. Bennett，A. Carbery，A.鲁伊斯和M. C. Vilela关于确定$s\geq0$和$p\geq1$上的最佳范围的问题，对于该最佳范围，下面的具有时间依赖性权重$w$的Morrey-Campanato型类$\mathfrak{L}^{2s+2,p}_2$中的Mashartz估计成立：\begin{equation}\label{absset} \|e^{itΔ}f\|_{L_{x,t}^2(w(x,t))}\leq C\|w\|_{\mathfrak{L}^{2s+2,p}_2}^{1/2}\|f\|_{\dot{H}^s}. \end{equation}在$s\geq0$的情况之外，我们进一步询问我们可以期望在此设置上有多大的规律性。但有趣的是，事实证明，只要$s<0$，这个估计是错误的，这表明平滑效应不能发生在这个时间依赖的设置和色散薛定谔流$e^{itΔ}$是不够强，有效果。这自然会导致我们考虑在最好的高阶版本的估计与$e^{-it(-Δ)^{γ/2}}$（$γ>2$），其色散更强的效果的可能性。我们确实获得了这些高阶版本的平滑效果。实际上，我们将得到其中$γ\geq1$以统一的方式的估计以及它们相应的非齐次估计，从而应用于薛定谔方程和含时扰动波动方程的整体适定性.这是本文的第二个目的。
