Introduction to Fourier Analysis on Euclidean SpacesThe authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces. |
Contents
The Fourier Transform | 1 |
Boundary Values of Harmonic Functions | 37 |
The Theory of HP Spaces on Tubes | 89 |
Symmetry Properties of the Fourier Transform | 133 |
Interpolation of Operators | 177 |
Singular Integrals and Systems of Conjugate | 217 |
Multiple Fourier Series | 245 |
| 287 | |
| 295 | |
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Introduction to Fourier Analysis on Euclidean Spaces Elias M. Stein,Guido Weiss Limited preview - 1971 |
Common terms and phrases
analytic function argument Banach space belongs Borel measure boundary values bounded Chapter characteristic function cone consider continuous function convergence convolution Corollary denote domain En+1 equality everywhere exists a constant extend fact finite Borel measure Fourier series Fourier transform function defined function f harmonic functions Hilbert transform immediate consequence implies inequality interpolation theorem L¹(E L¹(En Lemma linear operators LP norm mapping Marcinkiewicz maximal function Moreover n-tuple nonnegative nontangential limits norm obtain orthogonal P₁ Plancherel theorem Poisson integral Poisson kernel Poisson summation formula polynomials proof of Theorem proved radial real numbers restricted rotation satisfying singular integral spherical harmonics subharmonic subset suffices to show summability Suppose tempered distribution tends testing function Theorem 1.1 theory tube unit sphere variables y₁ Zygmund ΜΕΛ Ση