Abstract
Various important inequalities, such as Bernstein, Kolmogorov, Marcinkiewicz–Zygmund, Nikolskii, and so on, have been proved in the usual Lebesgue spaces on the sphere. The main purpose of this paper is to prove analogues of these results. We establish analogous inequalities in Lebesgue spaces with variable exponents on the sphere.
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Notes
There is a mistake in the proof of [17, Theorem 8.1]. However, Kolmogorov-type inequalities on the sphere are true.
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The first author was partially supported by China Scholarship Council (Grant No. CSC201906315017) and the Fundamental Research Funds for the Central Universities (Grant No. 20720190062). The second author was supported by the National Natural Science Foundation of China (Project no. 11671271) and the Natural Science Foundation of Beijing Municipality.
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Huang, H., Wang, H. Polynomial Inequalities in Lebesgue Spaces with Variable Exponents on the Sphere. J Geom Anal 32, 33 (2022). https://doi.org/10.1007/s12220-021-00786-y
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DOI: https://doi.org/10.1007/s12220-021-00786-y