Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63), Volume 63

Contents\nPreface\nIntroduction\nChapter I. Lie Groups (A Review)\n	§1. Compact groups\n	§2. The Peter-Weyl theorem\n	§3. The Peter-Weyl theorem (Concluded)\n	§4. Lie groups; examples\n	§5. Lie algebras\n	§6. Universal enveloping algebra\n	§7. Laplacian\nChapter II. Littlewood-Paley Theory for a Compact Lie Group\n	§1. The heat-diffusion semi-group\n	§2. The Poisson semi-group; the main theorem\n	3. Proof of Theorem 2\n	§4. Applications: Riesz transforms, etc\n	Bibliographical remarks\nChapter III. General Symmetric Diffusion Semi-groups\n	§1. General setting\n	§2. Analyticity of these semi-groups\n	§3. The maximal theorem\n	§4. A digression: L2 theorems\n	Bibliographical remarks\nChapter IV. The General Littlewood-Paley Theory\n	§1. Conditional Expectation and Martingales\n	§2. The inequalities for martingales\n	§3. An additional ‘‘max’’ inequality\n	§4. The link between martingales and semi-groups\n	§5. The Littlewood-Paley inequalities in general\n	§6. Dénouement\n	Bibliographical remarks\nChapter V. Further Illustrations\n	§1. Lie groups\n	§2. Semi-simple case\n	§3. Sturm-Liouville\n	§4. Heuristics\n	Bibliographical remarks\nReferences\nAppendix (1985)