An eigenfunction stability estimate for approximate extremals of the Bellman function for the dyadic maximal operator on 𝐿^{𝑝}

Melas, Antonios

doi:10.1090/proc12740

An eigenfunction stability estimate for approximate extremals of the Bellman function for the dyadic maximal operator on $L^{p}$
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Proc. Amer. Math. Soc. 147 (2019), 3367-3375 Request permission

Abstract:

We prove a stability estimate for the functions that are almost extremals for the Bellman function related to the $L^{p}$ norm of the dyadic maximal operator in the case $p\geq 2$. This estimate gives that such almost extremals are also almost “eigenfunctions” for the dyadic maximal operator, in the sense that the $L^{p}$ distance between the maximal operator applied to the function and a certain multiple of the function is small.

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