Harmonic Analysis on Euclidean Spaces

Code: MA649 | L-T-P-C: 3-0-0-6

Prerequisites: MA 550 Measure Theory or MA224 Real Analysis

Course Content/ Syllabus Distribution function, decreasing rearrangements weak Lp spaces and Lorentz Spaces, Marcinkiewicz Interpolation Theorem, Riesz–Thorin Interpolation Theorem and Interpolation of Analytic Families of Operators, Off-Diagonal Marcinkiewicz Interpolation Theorem, Hardy–Littlewood Maximal Operator and Lebesgue differentiation Theorem, Class of Schwartz Functions, Class of Tempered Distributions and their Fourier transform; Convolution Operators on Lp Spaces and Multipliers, Hilbert Transform and Riesz Transforms, Homogeneous Singular and Maximal Singular Integrals, Calderon–Zygmund Decomposition and Singular Integrals.

Texts:

1. Javier Duoandikoetxea, Fourier Analysis, GSM Vol 29 AMS 2000
2. Loukas Grafakos, Classical Fourier Analysis, 2nd Edition, Springer 2000

References:

1. Elias M Stein, Harmonic Analysis, Princeton University Press 1993
2. Elias M Stein and Rami Shakarchi, Functional Analysis, Princeton University Press 2011