https://paura.se/notes/New lecture notes and seminar solutions as they are published.en-usFri, 11 Sep 2026 00:00:00 -0500https://paura.se/read/harmonic-analysis-lecture-4/The Schwartz class and tempered distributions, differentiation and convolution on 𝒮', the Fourier transform, translation-invariant operators, the Hilbert and Riesz transforms, and the Calderón–Zygmund decomposition.Fri, 11 Sep 2026 00:00:00 -0500https://paura.se/read/harmonic-analysis-lecture-4/Harmonic AnalysisLectureshttps://paura.se/read/harmonic-analysis-seminar-1-solutions/Five exercises worked in full: the M_c f ≤ Mf ≤ 2^d M_c f comparison, lower semicontinuity of Mf, L^q + L^r ⊆ L^1_loc, convergence of the averages f_r, and the oscillation bound leading to Lebesgue differentiation.Wed, 09 Sep 2026 00:00:00 -0500https://paura.se/read/harmonic-analysis-seminar-1-solutions/Harmonic AnalysisSeminar solutionshttps://paura.se/read/harmonic-analysis-lecture-3/The Lebesgue differentiation theorem, the resulting L^p bounds on the maximal function, and approximate identities.Tue, 08 Sep 2026 00:00:00 -0500https://paura.se/read/harmonic-analysis-lecture-3/Harmonic AnalysisLectureshttps://paura.se/read/harmonic-analysis-lecture-2/Decomposing L^p into L^q + L^r, linear and sublinear operators, weak and strong type, and the Marcinkiewicz interpolation theorem.Fri, 04 Sep 2026 00:00:00 -0500https://paura.se/read/harmonic-analysis-lecture-2/Harmonic AnalysisLectureshttps://paura.se/read/harmonic-analysis-lecture-1/Locally integrable functions, the centred and uncentred Hardy–Littlewood maximal functions, and the comparison between them.Tue, 01 Sep 2026 00:00:00 -0500https://paura.se/read/harmonic-analysis-lecture-1/Harmonic AnalysisLectures