Research profile
Winston Ou
Author of work recommended on this site.
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- on the reading lists
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On the reading lists
What this site's guides and courses recommend by Winston Ou, and why. Each opens its Library entry.
- A good place to startVideoFunctional Analysis Lecture 04: Dual L^p spaces
The dual of Lᵖ is Lᵖ′.
Recommended in Guidebook 4A.4: Hahn–Banach and Duality
- VideoFunctional Analysis Lecture 06: Riesz Interpolation Theorem, Part 1
Riesz–Thorin interpolation, the three lines lemma and Hausdorff–Young. (The lecturer notes that the exponents in the board statement need not be conjugate.)
Recommended in Guidebook 4A.12: Interpolation and Fractional Sobolev Spaces
- VideoFunctional Analysis Lecture 07: Riesz Interpolation Theorem, Part 2
The proof of Riesz–Thorin completed.
Recommended in Guidebook 4A.12: Interpolation and Fractional Sobolev Spaces
- VideoFunctional Analysis Lecture 10: Lᵖ boundedness of the Maximal Function
The Hardy–Littlewood maximal function and its Lᵖ bounds, proved with a covering lemma.
Recommended in Guidebook 3A.6: Modes of Convergence and Differentiation
- VideoFunctional Analysis Lecture 15: Operations on Distributions; Tempered distributions
Differentiating and convolving distributions.
Recommended in Guidebook 4A.9: Distributions and Weak Derivatives
- VideoFunctional Analysis Lecture 16: Tempered Distributions
Tempered distributions and their Fourier transforms.
Recommended in Guidebook 4A.9: Distributions and Weak Derivatives
- VideoFunctional Analysis Lecture 21: Lᵖ boundedness of Singular Integrals
Why singular integrals are bounded on Lᵖ.
Recommended in Guidebook 6B.8: Lᵖ Theory and Strong Solutions
- VideoFunctional Analysis Lecture 22: Lᵖ boundedness of Singular Integrals, continued
The Calderón–Zygmund argument completed.
Recommended in Guidebook 6B.8: Lᵖ Theory and Strong Solutions
- VideoFunctional Analysis Lecture 25: More applications of the Baire Category Theorem
Continuous functions whose Fourier series diverge on a dense set are generic, and the open mapping theorem.
Recommended in Guidebook 4A.2: Baire Category and Its Consequences
- VideoMath 139 Fourier Analysis, Lecture 05: Convolutions and Approximation of the Identity
The approximate identities that make mollifiers work.
Recommended in Guidebook 3A.8: Convolution and Mollifiers
- VideoMath 139 Fourier Analysis, Lecture 15: The Fourier Transform
The Fourier transform on ℝ, its definition and first properties.
Recommended in Guidebook 4A.6: The Fourier Transform
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NP-RC-995211 is Winston Ou's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.
A window on one part of a person's work: papers here go back to 2021 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. If two people share this name, their work may appear together here. How it is put together.