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- W2963172964 abstract "Let $L= -Delta+ V$ be a Schrodinger operator on $mathbb R^d$, $dgeq 3$, where $V$ is a nonnegative potential, $Vne 0$, and belongs to the reverse Holder class $RH_{d/2}$. In this paper, we study the commutators $[b,T]$ for $T$ in a class $mathcal K_L$ of sublinear operators containing the fundamental operators in harmonic analysis related to $L$. More precisely, when $Tin mathcal K_L$, we prove that there exists a bounded subbilinear operator $mathfrak R= mathfrak R_T: H^1_L(mathbb R^d)times BMO(mathbb R^d)to L^1(mathbb R^d)$ such that begin{equation}label{abstract 1}|T(mathfrak S(f,b))|- mathfrak R(f,b)leq |[b,T](f)|leq mathfrak R(f,b) + |T(mathfrak S(f,b))|,end{equation}where $mathfrak S$ is a bounded bilinear operator from $H^1_L(mathbb R^d)times BMO(mathbb R^d)$ into $L^1(mathbb R^d)$ which does not depend on $T$. The subbilinear decomposition (ref{abstract 1}) allows us to explain why commutators with the fundamental operators are of weak type $(H^1_L,L^1)$, and when a commutator $[b,T]$ is of strong type $(H^1_L,L^1)$.Also, we discuss the $H^1_L$-estimates for commutators of the Riesz transforms associated with the Schrodinger operator $L$." @default.
- W2963172964 created "2019-07-30" @default.
- W2963172964 creator A5077690287 @default.
- W2963172964 date "2015-01-01" @default.
- W2963172964 modified "2023-09-28" @default.
- W2963172964 title "Endpoint estimates for commutators of singular integrals related to Schrödinger operators" @default.
- W2963172964 doi "https://doi.org/10.4171/rmi/871" @default.
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