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arXiv · 2401.00398

Interpolation on Convex-set Valued Lebesgue Spaces and its Applications

Yuxun Zhang·Jiang Zhou
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Abstract

In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As applications, we obtain the boundedness of convex-set valued fractional averaging operators and fractional maximal operators, and prove the reverse factorization property of matrix weights.

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Yuxun Zhang, Jiang Zhou. 2023-12-31. Interpolation on Convex-set Valued Lebesgue Spaces and its Applications. https://arxiv.org/abs/2401.00398

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