Second-order Riesz Transforms and Maximal Inequalities Associated with Magnetic Schrodinger Operators

Let A:=-(del - i (a) over right arrow).(del - i (a) over right arrow )+V be a magnetic Schrodinger operator on R-n, where (a) over right arrow:= (a(1),(...),a(n)) epsilon L-loc(2)(R-n,R-n) and 0 <= V epsilon L-loc(1)(R-n) satisfy some reverse Holder conditions. Let phi:R(n)x[0,infinity) -> [0,infinity) be such that phi(x,.) for any given x epsilon R-n is an Orlicz function, phi(.,t)epsilon A(infinity)(R-n) for all t epsilon(0,infinity) (the class of uniformly Muckenhoupt weights) and its uniformly critical upper type index I(phi)epsilon(0,1]. In this article, the authors prove that second-order Riesz transforms VA-(1) and (del-i (a) over right arrow)(2)A-(1) are bounded from the Musielak-Orlicz-Hardy space H-phi,H-A(R-n), associated with A, to the Musielak-Orlicz space L-phi(R-n). Moreover, the authors establish the boundedness of VA-(1) on H-phi,H-A(R-n). As applications, some maximal inequalities associated with A in the scale of H-phi,H-A(R-n) are obtained.