A multiparameter integral inequality for the dyadic maximal operator and applications

2019/05/17 by Eleftherios N. Nikolidakis, Nikolidakis, Eleftherios N.
Mathematics · #42B25 #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1905.08091

openalex publication_date 2019/05/17 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We prove a sharp multiparameter integral inequality for the dyadic maximal operator which refines the one-parameter inequality that is given by A.Melas in [4] which in turn is applied for the evaluation of the Bellman function of two integral variables for this maximal operator. Moreover we find the exact domain of definition of the related Bellman function of three integral variables and by using the results connected with the sharpness of this new multiparameter inequality we give lower bounds of this Bellman function.

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