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Math 6081A, Fall 2017
Welcome to Math 6081A, Topics in Harmonic Analysis
In this course, we will cover some basics of harmonic analysis. We will start with the Fourier transform, tempered distributions, and harmonic functions, and move on to maximal functions, fractional integrals, singular integrals, and pseudodifferential operators. Along the way we will encounter function spaces like Sobolev spaces, Hölder spaces and BMO. We will also prove the T(1) theorem and discuss interpolation. Most of the material can be found in the following reference books:
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J. Duoandikoetxea, "Fourier Analysis"
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C. Muscalu and W. Schlag, "Classical and Multilinear Harmonic Analysis" (volume I)
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E.M. Stein, "Singular integrals and differentiability properties of functions"
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E.M. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals"
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T. Wolff, "Lectures on Harmonic Analysis"
Lecture notes:
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Lecture 1: The Fourier transform (last updated: Sept 14, 2017)
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Lecture 2: Tempered distributions and Harmonic functions (last updated: Sept 22, 2017)
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Lecture 3: Maximal functions and Riesz potentials (last updated: Feb 22, 2018)
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Lecture 4: Singular integrals and Littlewood-Paley decompositions (last updated: Dec 21, 2017)
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Lecture 5: Hölder spaces, Sobolev spaces and BMO functions (last updated: Dec 21, 2017)
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Lecture 6: Pseudodifferential calculus and almost orthogonality (last updated: Mar 9, 2018)
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Lecture 7: Paraproducts, Carleson measures, and the T(1) theorem (last updated: Mar 6, 2018)
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Lecture 8: Interpolation (last updated: August 12, 2019)
Homework:
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