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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.


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


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