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In this paper, we establish a good-$\lz$ inequality with two parameters inthe Schr\"odinger settings. As it's applications, we obtain weighted estimatesfor spectral multipliers and Littlewood-Paley operators and their commutatorsin the Schr\"odinger settings.

Weighted norm inequalities, spectral multipliers and Littlewood-Paley operators in the Schr\"odinger settings