Geodesic
A note on Poincaré constants
Filomat, Tome 36 (2022) no. 16, p. 5463

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DOI

In this note, we give two comparison results of Poincaré constants: (i) Let X and Y be Banach spaces. We give a relationship between the X-valued p-Poincaré constant and the Y-valued q-Poincaré constant introduced by Laat and Salle for all 1 ≤ p, q ∞ when the unit sphere S(X) of X is uniformly homeomorphic to the unit sphere S(Y) of Y. (ii) We provide an explicit relationship between the nonlinear spectral gap introduced by Mimura and the Poincaré constant introduced by Laat and Salle.
DOI : 10.2298/FIL2216463C
Classification : 46B80, 46B85
Keywords: Banach space, unit sphere, sphere equivalence, extrapolation, Poincaré constant 
Junxi Chen; Xiaoyu Cheng. A note on Poincaré constants. Filomat, Tome 36 (2022) no. 16, p. 5463 . doi: 10.2298/FIL2216463C
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     author = {Junxi Chen and Xiaoyu Cheng},
     title = {A note on {Poincar\'e} constants},
     journal = {Filomat},
     pages = {5463 },
     year = {2022},
     volume = {36},
     number = {16},
     doi = {10.2298/FIL2216463C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2216463C/}
}
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