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Orlicz estimates for parabolic Schrödinger operators with non-negative potentials on nilpotent Lie groups
AIMS Mathematics 2023, 8(8): 18631-18648
Published: 15 August 2023
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In this paper, we study the Orlicz estimates for the parabolic Schrödinger operator

L = t Δ X + V ,

where the nonnegative potential V belongs to a reverse Hölder class on nilpotent Lie groups G and Δ X is the sub-Laplace operator on G . Under appropriate growth conditions of the Young function, we obtain the regularity estimates of the operator L in the Orlicz space by using the domain decomposition method. Our results generalize some existing ones of the L p estimates.

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