Abstract
Let L = −Δ + V be a Schrödinger operator on ℝn, where V is a nonnegative potential satisfying the suitable reverse Hölder’s inequality. In this paper, we study the boundedness of the second order Riesz transforms such as L−1∇2on the spaces of BMO type for weighted case. We generalized the known results to the weighted case.
Highlights
Introduction and preliminariesThe study of both function spaces and the boundedness of singular integral operators associated with Schrödinger operators arose from practical applications in some mathematical fields, such as harmonic analysis and partial differential equations, and has become an active area of research in the last few years
These type of questions have been already considered by many authors and they are very important questions which appeal to various techniques from partial differential equations and harmonic analysis
Many authors have been interested in the problems of harmonic analysis associated with Schrödinger operators on Rn, see [1,2,3, 5, 6, 12, 14,15,16,17, 19, 21, 25]
Summary
The study of both function spaces and the boundedness of singular integral operators associated with Schrödinger operators arose from practical applications in some mathematical fields, such as harmonic analysis and partial differential equations, and has become an active area of research in the last few years. These type of questions have been already considered by many authors and they are very important questions which appeal to various techniques from partial differential equations and harmonic analysis. By Theorem 1.7 in [8], the authors proved that L−1∇2 is bounded on the Note that, since BMOβL(ω) ⊂ BMOβ(ω), our results can be considered as improvements of those in [8], even in the case ω ≡ 1.
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