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 John-Nirenberg'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:
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arXiv e-prints
- Pub Date:
- November 2022
- DOI:
- 10.48550/arXiv.2212.00681
- arXiv:
- arXiv:2212.00681
- Bibcode:
- 2022arXiv221200681N
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- Small fixes and keywords