Abstract
In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to \(p\)-quermassintegrals so that the cases \(p=1, -1, -n\) of \(p\)-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with \(p\)-quermassintegrals, including \(L_q\) Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality.
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Acknowledgments
The authors sincerely thank the reviewer for very valuable and helpful comments and suggestions, which have made the paper more accurate and readable.
Funding
This research was supported in part by the Natural Science Foundation of China (Grant Nos. 11371224, 11901346).
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2023, Vol. 57, pp. 18–30 https://doi.org/10.4213/faa4065.
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Wang, W., Zhou, Y. Some Inequalities for \(p\)-Quermassintegrals. Funct Anal Its Appl 57, 99–108 (2023). https://doi.org/10.1134/S0016266323020028
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DOI: https://doi.org/10.1134/S0016266323020028