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| Let $A:=-(
abla-i ec{a})cdot(
abla-i ec{a})+V$be a magnetic Schr"odinger operator on $mathbb{R}^n$, where$ ec{a}:=(a_1,,ldots,, a_n)inL^2_{mathrm{loc}}(mathbb{R}^n,mathbb{R}^n)$ and $0le VinL^1_{mathrm{loc}}(mathbb{R}^n)$ satisfy some reverse H"olderconditions. Let $ arphi:\mathbb{R}^n imes[0,infty) o[0,infty)$ be such that$ arphi(x,cdot)$ for any given $xinmathbb{R}^n$ is an Orliczfunction, $ arphi(cdot,t)in {mathbb A}_{infty}(mathbb{R}^n)$for all $tin (0,infty)$ (the class of uniformly Muckenhouptweights) and its uniformly critical upper type index$I( arphi)in(0,1]$. In this article, the authors prove thatsecond-order Riesz transforms $VA^{-1}$ and$(
abla-i ec{a})^2A^{-1}$ are bounded from theMusielak-Orlicz-Hardy space $H_{ arphi,,A}(mathbb{R}^n)$,associated with $A$, to the Musielak-Orlicz space$L^{ arphi}(mathbb{R}^n)$. Moreover, the authors establish theboundedness of $VA^{-1}$ on $H_{ arphi,,A}(mathbb{R}^n)$. Asapplications, some maximal inequalities associated to $A$ in thescale of $H_{ arphi,,A}(mathbb{R}^n)$ are obtained. |
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| Keywords:Musielak-Orlicz-Hardy space,magnetic Schr"odinger operator, atom, second-orderRiesz transform, maximal inequality |
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