MSC2020 · 42Bxx

Harmonic analysis in several variables

Harmonic analysis in several variables \{For automorphic theory, see mainly 11F30\}

5 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

42B05Fourier series and coefficients in several variables0 42B08Summability in several variables0 42B10Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type2 42B15Multipliers for harmonic analysis in several variables1 42B20Singular and oscillatory integrals (Calderón-Zygmund, etc.)1 42B25Maximal functions, Littlewood-Paley theory1 42B30

H^p

-spaces0 42B35Function spaces arising in harmonic analysis0 42B37Harmonic analysis and PDEs0 42B99Harmonic analysis in several variables0

Mapped problems

OP-12116AnalysisStatus unassessed

Uncertainty principle (AlphaEvolve problem 11)

Uncertainty principle (AlphaEvolve problem 11). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12092AnalysisOpen

3D critical Bochner–Riesz exponent ( $C_{77}$ )

3D critical Bochner–Riesz exponent: determine C 77 or improve its bounds; the repository records 3 (lower) and frac 13 4 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12066AnalysisOpen

Beurling–Ahlfors transform constant ( $C_{54}$ )

Beurling–Ahlfors transform constant: determine C 54 or improve its bounds; the repository records 1 (lower) and 1.575 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12059AnalysisOpen

Centered Hardy-Littlewood maximal constant in dimension $2$ ( $C_{47}$ )

Centered Hardy-Littlewood maximal constant in dimension 2 : determine C 47 or improve its bounds; the repository records 1.68550999 (lower) and 3.879 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12058AnalysisOpen

Fourier restriction constant for the 2-sphere ( $C_{46}$ )

Fourier restriction constant for the 2-sphere: determine C 46 or improve its bounds; the repository records 3 (lower) and frac 22 7 approx 3.142857 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

Journals & articles in MSC 42

These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.

Analysis & PDE ↗

Mathematical Sciences Publishers

Analysis and partial differential equations

Journal discovery is available; article-level extraction for this class is not yet included in this batch.

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Subcategories

Mapped problems

Uncertainty principle (AlphaEvolve problem 11)

3D critical Bochner–Riesz exponent (C77C_{77}C77​)

Beurling–Ahlfors transform constant (C54C_{54}C54​)

Centered Hardy-Littlewood maximal constant in dimension 222 (C47C_{47}C47​)

Fourier restriction constant for the 2-sphere (C46C_{46}C46​)

Journals & articles in MSC 42

3D critical Bochner–Riesz exponent ( $C_{77}$ )

Beurling–Ahlfors transform constant ( $C_{54}$ )

Centered Hardy-Littlewood maximal constant in dimension $2$ ( $C_{47}$ )

Fourier restriction constant for the 2-sphere ( $C_{46}$ )