Bounded Mean Oscillation: an $\mathbb{R}$-Function with Multi-$\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent

Edoardo Niccolai

Bounded Mean Oscillation: an $\mathbb{R}$-Function with Multi-$\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent

Functional Analysis 2023-02-08 v2

Authors: Edoardo Niccolai

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.

Keywords

bounded mean oscillation harmonic functions hardy space h1 john-nirenberg exponential integrability duality banach space

Cite

@article{arxiv.2212.00681,
  title  = {Bounded Mean Oscillation: an $\mathbb{R}$-Function with Multi-$\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent},
  author = {Edoardo Niccolai},
  journal= {arXiv preprint arXiv:2212.00681},
  year   = {2023}
}

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Small fixes and keywords

Bounded Mean Oscillation: an $\mathbb{R}$-Function with Multi-$\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent

Abstract

Keywords

Cite

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