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Topic · Applied Mathematics

Advanced Harmonic Analysis Research

Advanced Harmonic Analysis Research is a research topic within Applied Mathematics. Science Explorer counts 13k research works in it since 1950. 13.6% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers topics in harmonic analysis and operator theory, including Fourier multiplier theorems, Calderón–Zygmund theory, maximal operators, Hardy spaces, singular integrals, Morrey spaces, boundedness of operators, elliptic operators, weighted estimates, and various function spaces.

  • Fourier Multiplier Theorems
  • Calderón–Zygmund Theory
  • Maximal Operators
  • Hardy Spaces
  • Singular Integrals
  • Morrey Spaces
  • Boundedness
  • Elliptic Operators
  • Weighted Estimates
  • Function Spaces
Research works
13k
fractional, since 1950
In the world top 10%
1.8k
per year above
Top-10% rate
13.6%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+7%
the tick is no change

Which countries lead Advanced Harmonic Analysis Research research?

By volume, China and the United States publish the most (460 and 172 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 460 works
  2. 2 United States 172 works
  3. 3 India 115 works
  4. 4 Russia 111 works
  5. 5 Spain 82 works
  6. 6 Türkiye 79 works
  7. 7 Italy 68 works
  8. 8 Germany 66 works
  9. 9 Japan 64 works
  10. 10 France 57 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 36.1%United States: 13.5%India: 9.0%Russia: 8.7%6 others listed: 32.7%36%largest
China460 · 36.1%United States172 · 13.5%India115 · 9.0%Russia111 · 8.7%6 others listed416 · 32.7%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Harmonic Analysis Research research?

By volume in 2022–2025, Beijing Normal University publishes the most Advanced Harmonic Analysis Research research, followed by Xinjiang University and Northwest Normal University.

By volume, 2022–2025

  1. 1 Beijing Normal UniversityChina 30 works
  2. 2 Xinjiang UniversityChina 16 works
  3. 3 Northwest Normal UniversityChina 12 works
  4. 4 Ghent UniversityBelgium 12 works
  5. 5 Education University of Hong KongHong Kong 12 works
  6. 6 Central South UniversityChina 11 works
  7. 7 Zhejiang Normal UniversityChina 11 works
  8. 8 Sun Yat-sen UniversityChina 10 works
  9. 9 St Petersburg UniversityRussia 10 works
  10. 10 Steklov Mathematical InstituteRussia 10 works

Who are the leading researchers in Advanced Harmonic Analysis Research?

The most-cited researchers publishing on Advanced Harmonic Analysis Research include Terence Tao, Ronald R. Coifman and Brian Street.

  1. 1 Terence Tao United States 3.1k citations
  2. 2 Ronald R. Coifman United States 2k citations
  3. 3 Brian Street United Kingdom 1.9k citations
  4. 4 Jean Bourgain United States 1.4k citations
  5. 5 H. M. Srivastava Canada 1.4k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Advanced Harmonic Analysis Research research done?

The largest centres of Advanced Harmonic Analysis Research research in 2022–2025 are Beijing (China), Moscow (Russia), Guangzhou (China) and Seoul (South Korea).

Largest cities, 2022–2025

  1. 1 Beijing China 79 works
  2. 2 Moscow Russia 40 works
  3. 3 Guangzhou China 25 works
  4. 4 Seoul South Korea 22 works
  5. 5 Baku Azerbaijan 22 works
  6. 6 Warsaw Poland 21 works
  7. 7 Changsha China 21 works
  8. 8 Madrid Spain 21 works
  9. 9 Lanzhou China 19 works
  10. 10 Hangzhou China 18 works
See Advanced Harmonic Analysis Research on the map

Where is the best place to study Advanced Harmonic Analysis Research?

Among universities, judged by research, Education University of Hong Kong, Beijing Normal University and Ghent University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 17.25%fractional works in this node (log) →share in the world top 10% →Education University of Hong Kong: 12, 47.1%Beijing Normal University: 30, 44.0%Ghent University: 12, 5.0%Macquarie University: 9, 16.1%L. N. Gumilyov Eurasian National University: 9, 5.3%Xinjiang University: 16, 12.3%Northwest Normal University: 12, 20.7%University Mohamed Boudiaf of M'sila: 9, 5.7%Zhejiang Normal University: 11, 7.1%Southern Federal University: 8, 9.2%Education University…Beijing Normal Unive…Macquarie UniversityGhent University
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Education University of Hong KongHong Kong 85.047.1%41.0×12 +356.2%
2 Beijing Normal UniversityChina 77.644.0%22.2×30 -18.4%
3 Ghent UniversityBelgium 51.45.0%10.8×12 +136.0%
4 Macquarie UniversityAustralia 49.716.1%13.3×9 +72.7%
5 L. N. Gumilyov Eurasian National UniversityKazakhstan 47.45.3%31.6×9 +198.9%
6 Xinjiang UniversityChina 44.012.3%19.2×16 +11.5%
7 Northwest Normal UniversityChina 43.720.7%25.7×12 -9.4%
8 University Mohamed Boudiaf of M'silaAlgeria 41.15.7%86.5×9 +115.4%
9 Zhejiang Normal UniversityChina 39.07.1%19.5×11 +29.5%
10 Southern Federal UniversityRussia 35.99.2%24.6×8 +47.7%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Advanced Harmonic Analysis Research research growing?

Output in 2018–2022 was 7% higher than in 2013–2017, peaking in 2022. The fastest-growing topics are Advanced Harmonic Analysis Research.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.