ENDPOINT ESTIMATES FOR COMMUTATORS OF RIESZ TRANSFORMS ASSOCIATED WITH SCHRODINGER OPERATORS

In this paper, we discuss the H(L)(1)-boundedness of commutators of Riesz transforms associated with the Schrodinger operator L = -Delta + V, where H(L)(1)(R(n)) is the Hardy space associated with L. We assume that V(x) is a nonzero, nonnegative potential which belongs to B(q) for some q > n/2. Let = V (x)(-Delta + V)(-1), T(2) = V(1/2)(-Delta + V)(-1/2) and T(3) = del(-Delta + V)(-1/2). We prove that, for b epsilon BMO(R(n)), the commutator [b, T(3)] is not bounded from H(L)(1)(R(n)) to L(1) (R(n)) as T(3) itself. As an alternative, we obtain that [b, T(i)],( i = 1, 2, 3) are of (H(L)(1), L(weak)(1))-boundedness.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000285121700002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)9ARTICLE3367-3898