2016/07/11 by Eleftherios N. Nikolidakis, Nikolidakis, Eleftherios N.
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1607.03033
openalex publication_date 2016/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a sharp integral inequality for the dyadic maximal operator due to\nwhich the evaluation of the Bellman function of this operator with respect to\ntwo variables is possible, as can be seen in [3]. Our inequality of interest is\nproved in this article by a simpler and more immediate way. We also study a\nstability result in connection with this inequality, that is we provide a\nnecessary and sufficient condition, for a sequence of functions,under which we\nobtain equality in the limit. The proof of this result is based on the proof of\nthe related inequality which we present in this article.\n