Bounded Mean Oscillation: an $\mathbb{R}$Function with Multi$\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent
Abstract
This paper investigates the concept of harmonic functions of bounded mean oscillation, starting from JohnNirenberg's pioneering studies, under a renewed formalism, suitable for bringing out some fundamental properties inherent in it. In more detail: after a quick introduction, the second Section presents the main theorem, plus complete proof, relating to this function; in the third Section there is a suggestion on the exponential integrability (theorem and sketch of proof), while the fourth Section deals with the duality of Hardy Space $H^1$ and bounded mean oscillation, with some ideas for a demonstration. The writing closes with a graphic appendix.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2212.00681
 arXiv:
 arXiv:2212.00681
 Bibcode:
 2022arXiv221200681N
 Keywords:

 Mathematics  Functional Analysis
 EPrint:
 Small fixes and keywords