Extension of quasi-Holder embeddings between unit spheres of p-normed spaces

In this paper, we introduce and study the quasi-Holder mappings between unit spheres of p-normed spaces. The quasi-Holder map is a natural generalization of the Holder map, Lipschitz map, quasi-isometry and e-isometry, etc. Concretely, we study the extension of a quasi-Holder embedding between unit spheres of p-normed spaces (0 < p <= 1) under the quasi-Holder or anti-Holder type assumption. We generalize the main results in Xiao and Lu (Ann Funct Anal 13(2):Paper No. 25, 2022) from the r-isometric case to the wider case of quasi-Holder mappings. Moreover, the method we adopted here is different; and the Hahn-Banach property, required as a condition in the main theorems of [30] has been removed in our results.

Automated summary

In this paper, we introduce and study the quasi-Holder mappings between unit spheres of p-normed spaces. The quasi-Holder map is a natural generalization of the Holder map, Lipschitz map, quasi-isometry and e-isometry, etc. We study the extension of a quasi-Holder embedding between unit spheres of p-normed spaces (0 < p <= 1) under the quasi-Holder or anti-Holder type assumption. We generalize the main results in Xiao and Lu (Ann Funct Anal 13(2):Paper No. 25, 2022) from the r-isometric case to the wider case of quasi-Holder mappings. Moreover, we adopt a different method and remove the Hahn-Banach property as a condition in our results.