An Introduction to the Theory of Multipliers

0. Prologue: The Multipliers for L1(G).- 0.0. Introduction.- 0.1. Multipliers for L1(G).- 0.2. Notation.- 0.3. Notes.- 1. The General Theory of Multipliers.- 1.0. Introduction.- 1.1. Elementary Theory of Multipliers.- 1.2. Characterizations of Multipliers.- 1.3. An Application: Multiplications which Preserve the Regular Maximal Ideals.- 1.4. Maximal Ideal Spaces.- 1.5. Integral Representations of Multipliers.- 1.6. Isometric Multipliers.- 1.7. Multipliers and Dual Spaces.- 1.8. The Derived Algebra.- 1.9. The Derived Algebra for Lp(G), 1? pM(Lp(G), Lq(G)), l?p, q??.- 5.5. Some Results Concerning Lp(G)^ and M(Lp(G), Lq(G))^.- 5.6. M(Lp(G), Lq(G)) as a Dual Space, 1?p, q??.- 5.7. Multipliers with Small Support.- 5.8. Notes.- 6. The Multipliers for Functions with Fourier Transforms in Lp (?).- 6.0. Introduction.- 6.1. The Banach Algebras Ap(G).- 6.2. The Multipliers for Ap(G) as Pseudomeasures.- 6.3. The Multipliers for Ap(G): G Noncompact.- 6.4. The Multipliers for Ap(G): G Compact.- 6.5. Notes.- 7. The Multipliers for the Pair (Hp(G), Hq (G)), 1?p, q??.- 7.0. Introduction.- 7.1. General Properties of M(Hp(G), Hq (G)), 1?p, q??.- 7.2. The Multipliers for the Pair (Hp(G), Hq (G)), 1?q?2?p??.- 7.3. The Multipliers for the Pair (Hp(G), H?(G)), 1?p??.- 7.4. Notes.- Appendices.- Appendix A: Topology.- Appendix B: Topological Groups.- Appendix C: Measure and Integration.- Appendix D: Functional Analysis.- Appendix E: Banach Algebras.- Appendix F: Harmonic Analysis.- Author and Subject Index.