Endpoint estimates for commutators of singular integrals related to Schrödinger operators
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Luong Dang Ky [1]
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[1] Quy Nhon University
Quy Nhon University
Vietnam
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 4, 2015, págs. 1333-1373
- Idioma: inglés
- DOI: 10.4171/RMI/871
- Texto completo no disponible (Saber más ...)
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Resumen
Let L=−Δ+V be a Schrödinger operator on Rd, d≥3, where V is a nonnegative potential, V≠0, and belongs to the reverse H\"older class RHd/2. In this paper, we study the commutators [b,T] for T in a class KL of sublinear operators containing the fundamental operators in harmonic analysis related to L. More precisely, when T∈KL, we prove that there exists a bounded subbilinear operator R=RT:H1L(Rd)×BMO(Rd)→L1(Rd) such that (⋆)|T(S(f,b))|−R(f,b)≤|[b,T](f)|≤R(f,b)+|T(S(f,b))|, where S is a bounded bilinear operator from H1L(Rd)×BMO(Rd) into L1(Rd) which does not depend on T. The subbilinear decomposition (⋆) allows us to explain why commutators with the fundamental operators are of weak type (H1L,L1), and when a commutator [b,T] is of strong type (H1L,L1).
Also, we discuss the H1L-estimates for commutators of the Riesz transforms associated with the Schrödinger operator L.
