Gagliardo-Nirenberg type inequalities on Lorentz, Marcinkiewicz and weak-𝐿^{∞} spaces

Dao, Anh; Lam, Nguyen; Lu, Guozhen

doi:10.1090/proc/15691

Gagliardo-Nirenberg type inequalities on Lorentz, Marcinkiewicz and weak-$L^{\infty }$ spaces
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by Anh Nguyen Dao, Nguyen Lam and Guozhen Lu PDF

Proc. Amer. Math. Soc. 150 (2022), 2889-2900 Request permission

Abstract:

We establish the Gagliardo-Nirenberg inequality, Trudinger-Moser inequality and John-Nirenberg inequality using the Lorentz spaces $L^{p,\alpha }$, the Marcinkiewicz space $L^{q,\infty }$ and the weak-$L^{\infty }$ space $W$ introduced by Bennett, DeVore and Sharpley [Ann. of Math. (2) 113 (1981), pp. 601–611]. As consequences, we obtain the Gagliardo-Nirenberg type inequality with weak-$L^{\infty }$ norm and BMO norm, Trudinger-Moser type inequality and John-Nirenberg type estimate with $BMO$ norm and weak-$L^{1}$ norm.

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