Uchiyama's decomposition of BMO functions is considered the "Mount Everest of Hardy space theory". This book is based on the draft, which the author completed before his sudden death in 1997. Nowadays, his contributions are extremely influential in various fields of analysis, leading to further breakthroughs.

Inhalt

Introduction.- 1. Lipschitz spaces and BMO.- 2. Atomic Hp spaces.- 3. Operators on Hp.- 4. Atomic decomposition from grand maximal functions.- 5. Atomic decomposition from S functions.- 6. Hardy-Littlewood-Fefferman-Stein type inequalities, 1.- 7. Hardy-Littlewood-Fefferman-Stein type inequalities, 2.- 8Hardy-Littlewood-Fefferman-Stein type inequalities, 3.- 9. Grand maximal functions from radial maximal functions.- 10 S-functions from g-functions.- 11. Good ? inequalities for nontangential maximal functions and S-functions of harmonic functions.- 14. Subharmonicity, 1.- 15. Subharmonicity, 2.- 16. Preliminaries for characterizations of Hp in terms of Fourier multipliers.- 17. Characterization of Hp in terms of Riesz transforms.- 18. Other results on the characterization of Hp in terms of Fourier multipliers.- 19. Fefferman's original proof of.- 20. Varopoulos's proof of the above inequality.- 21. The Fefferman-Stein decomposition of BMO.- 22. A constructive proof of the Fefferman-Stein decomposition of BMO.- 23. Vector-valued unimodular BMO functions.- 24. Extension of the Fefferman-Stein decomposition of BMO, 1.- 25. Characterization of H1 in terms of Fourier multipliers.- 26. Extension of the Fefferman-Stein decomposition of BMO, 2.- 27. Characterization of Hp in terms of Fourier multipliers.- 28. The one-dimensional case.- References.