Abstrakti
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.
Alkuperäiskieli | Englanti |
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Sivumäärä | 18 |
Julkaisu | PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A: MATHEMATICS |
DOI - pysyväislinkit | |
Tila | Sähköinen julkaisu (e-pub) ennen painettua julkistusta - 2021 |
OKM-julkaisutyyppi | A1 Julkaistu artikkeli, soviteltu |