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Grassmannian forms of LXYZ's $L^p$ affine Sobolev inequality chain

Part of: General convexity Linear function spaces and their duals

Published online by Cambridge University Press:  02 January 2026

Kai He  and
Ai-Jun Li
Kai He
Affiliation:
Zhejiang University of Science and Technology , China e-mail: 19851635186@163.com
Ai-Jun Li*
Affiliation:
Zhejiang University of Science and Technology , China e-mail: 19851635186@163.com
*
e-mail: liaijun72@163.com
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Abstract

In this article, we reformulate LXYZ’s $L^p$ affine Sobolev inequality chain (including Lutwak–Yang–Zhang’s $L^p$ affine Sobolev inequality and Xiao’s p-affine capacity inequality) in the setting of Grassmann manifolds. For this purpose, the Grassmannian $ p $-affine capacity is introduced.

Keywords

Lp affine Sobolev inequalityGrassmann manifoldGrassmannian p-affine capacity

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 17
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Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The second author was supported by NSFC (Grant Nos. 12571146 and 12231006).

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