Boundedness of functional calculi of Schrödinger operators on generalized Lebesgue spaces ${L^{p(cdot)}(mathbb{R}^n)}$

摘要

Let L = −Δ + V be a Schrödinger operator on ${mathbb{R}^n}$ , where ${Vin L^1_{rm loc}({mathbb R}^n)}$ is a nonnegative function on ${{mathbb{R}^n}}$ . Let ${L^{p(cdot)}(mathbb{R}^n)}$ be the generalized Lebesgue spaces. In this article we use a technical atomic decomposition of Hardy space associated with L to show that the L p(·)-norm of f can be controlled by the sum of the L p(·)-norms of two variants of sharp maximal functions of f. As a result, we obtain boundedness of functional calculi of Schrödinger operators on generalized Lebesgue spaces ${L^{p(cdot)}(mathbb{R}^n)}$ .