The boundedness of some integral operators on weighted Hardy spaces associated with Schrödinger operators

Details The boundedness of some integral operators on weighted Hardy spaces associated with Schrödinger operators The boundedness of some integral operators on weighted Hardy spaces associated with Schrödinger operators

2011-03-09

arxiv.org/abs/1103.1715v1

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this article, by using the atomic decomposition theory of weighted Hardy spaces $H^1_L(w)$ associated to $L$, we will obtain the imaginary power $L^{i\gamma}$ is bounded from $H^1_L(w)$ to $L^1(w)$ whenever $w\in A_1\cap RH_2$, and the fractional integral operator $L^{-\alpha/2}$ is bounded from $H^1_L(w)$ to $L^q(w^q)$, where $0<\alpha

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