| PrefaceCHAPTER Ⅰ The Fourier Transform1. The basic L1 theory of the Fourier transform2.The L2 theory and the Plancherel theorem3.The class of tempered distributions4.Further resultsCHAPTER Ⅱ Boundary Values of Harmonic Functions1.Basic properties of harmonic functions2.The characterization of Poisson integrals3.The Hardy-Littlewood maximal function and nontangential convergence of harmonic functions4.Subharmonic functions and majorization by harmonic functions 5.Further resultsCHAPTER Ⅲ The Theory of Hp Spaces on Tubes1.Introductory remarks2.The H2 theory3.Tubes over cones4.The Paley-Wiener theorem5.The Hp theory6.Further resultsCHAPTER Ⅳ Symmetry Properties of the Fourier Transform1.Decomposition of L2(Ez) into'sub, paces invariant under the Fourier transform2.Spherical harmonics3.The action of the Fourier transform on the spaces 4.Some applications5.Further resultsCHAPTER Ⅴ Interpolation of Operators1.The M. Riesz convexity theorem and interpolation of operators defined on Lp spaces2.The Marcinkiewicz interpolation theorem3.L(p, q) spaces4.Interpolation of analytic families of operators5.Further resultsCHAPTER Ⅵ Singular Integrals and Systems of Conjugate Harmonic Functions1.The Hilbert transform2.Singular integral operators with odd kernels3.Singular integral operators with even kernels4.Hp spaces of conjugate harmonic functions5.Further resultsCHAPTER Ⅶ Multiple Fourier Series1.Elementary properties2.The Poisson summation formula3.Multiplier transformations4.Summability below the critical index (negative results)5.Summability below the critical index6.Further resultsBibliographyIndex |
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