2021/07/01 by Juha Kinnunen, Kinnunen, Juha, Kim Myyryläinen +1
Computer Science · Mathematics · #42B25 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2107.00492
openalex publication_date 2021/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss the dyadic John-Nirenberg space that is a generalization of functions of bounded mean oscillation. A John-Nirenberg inequality, which gives a weak type estimate for the oscillation of a function, is discussed in the setting of medians instead of integral averages. We show that the dyadic maximal operator is bounded on the dyadic John-Nirenberg space and provide a method to construct nontrivial functions in the dyadic John-Nirenberg space. Moreover, we prove that the John-Nirenberg space is complete. Several open problems are also discussed.