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RIESZ TRANSFORMS AND LITTLEWOOD–PALEY SQUARE FUNCTION ASSOCIATED TO SCHRÖDINGER OPERATORS ON NEW WEIGHTED SPACES
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 105 / Issue 2 / October 2018
- Published online by Cambridge University Press:
- 18 June 2018, pp. 201-228
- Print publication:
- October 2018
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- Article
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Let
${\mathcal{L}}=-\unicode[STIX]{x1D6E5}+{\mathcal{V}}$ be a Schrödinger operator on 
$\mathbb{R}^{n},n\geq 3$, where 
${\mathcal{V}}$ is a potential satisfying an appropriate reverse Hölder inequality. In this paper, we prove the boundedness of the Riesz transforms and the Littlewood–Paley square function associated with Schrödinger operators 
${\mathcal{L}}$ in some new function spaces, such as new weighted Bounded Mean Oscillation (BMO) and weighted Lipschitz spaces, associated with 
${\mathcal{L}}$. Our results extend certain well-known results.
