a1 Department of Mathematics, Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira, Taipa, Macau, PR China (email: firstname.lastname@example.org)
a2 LMAM School of Mathematical Sciences, Peking University, Beijing 100871, PR China (email: email@example.com)
In this paper, we discuss the H1L-boundedness of commutators of Riesz transforms associated with the Schrödinger operator L=−△+V, where H1L(Rn) is the Hardy space associated with L. We assume that V (x) is a nonzero, nonnegative potential which belongs to Bq for some q>n/2. Let T1=V (x)(−△+V )−1, T2=V1/2(−△+V )−1/2 and T3 =∇(−△+V )−1/2. We prove that, for b∈BMO (Rn) , the commutator [b,T3 ] is not bounded from H1L(Rn) to L1 (Rn) as T3 itself. As an alternative, we obtain that [b,Ti ] , ( i=1,2,3 ) are of (H1L,L1weak) -boundedness.
(Received November 09 2008)
2000 Mathematics subject classification
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The first author was supported by the Macau Government Science and Technology Development Fund FDCT/014/2008/A1; the second author was supported by NNSF of China No. 10471002 and RFDP of China No. 20060001010.