Sharp Lorentz estimates for dyadic-like maximal operators and related\n Bellman functions

2015/11/19 by Antonios D. Melas, Melas, Antonios D., Eleftherios N. Nikolidakis +1
Mathematics · #42B25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1511.06112

openalex publication_date 2015/11/19 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We precisely evaluate Bellman type functions for the dyadic maximal opeator\non Rⁿ and of maximal operators on martingales related to local Lorentz type\nestimates. Using a type of symmetrization principle, introduced for the dyadic\nmaximal operator in earlier works of the authors we precisely evaluate the\nsupremum of the Lorentz quasinorm of the maximal operator on a function \φ\nwhen the integral of \φ is fixed and also the same Lorentz quasinorm of\n\φ is fixed. Also we find the corresponding supremum when the integral of\n\φ is fixed and several weak type conditions are given.\n

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