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RIESZ TRANSFORMS AND LITTLEWOOD–PALEY SQUARE FUNCTION ASSOCIATED TO SCHRÖDINGER OPERATORS ON NEW WEIGHTED SPACES

  • NGUYEN NGOC TRONG (a1) (a2) and LE XUAN TRUONG (a3)

Abstract

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.

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