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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. 10.0% 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%
1.3k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+10%
the tick is no change
Largest producer
China
37% of the 10 largest, 2022-now
Advanced Harmonic Analysis Research

Which countries lead Advanced Harmonic Analysis Research research?

By volume, China and the United States publish the most (545 and 207 works in 2022-now).

By volume, 2022-now

  1. 1 China 545 works
  2. 2 United States 207 works
  3. 3 India 131 works
  4. 4 Russia 121 works
  5. 5 Spain 89 works
  6. 6 Türkiye 84 works
  7. 7 Italy 80 works
  8. 8 Germany 76 works
  9. 9 Japan 70 works
  10. 10 France 68 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: 37.1%United States: 14.0%India: 8.9%Russia: 8.3%6 others listed: 31.7%37%largest
China545 · 37.1%United States207 · 14.0%India131 · 8.9%Russia121 · 8.3%6 others listed467 · 31.7%

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

Which institutions lead Advanced Harmonic Analysis Research research?

By volume in 2022-now, Beijing Normal University publishes the most Advanced Harmonic Analysis Research research, followed by Russian Academy of Sciences and Centre National de la Recherche Scientifique.

By volume, 2022-now

  1. 1 Beijing Normal UniversityChina 35 works
  2. 2 Russian Academy of SciencesRussia 35 works
  3. 3 Centre National de la Recherche ScientifiqueFrance 34 works
  4. 4 Xinjiang UniversityChina 18 works
  5. 5 Baylor UniversityUnited States 15 works
  6. 6 Northwest Normal UniversityChina 13 works
  7. 7 Central South UniversityChina 13 works
  8. 8 Ghent UniversityBelgium 13 works
  9. 9 Education University of Hong KongChina 13 works
  10. 10 Polish Academy of SciencesPoland 12 works

Who are the leading researchers in Advanced Harmonic Analysis Research?

The most-cited researchers publishing on Advanced Harmonic Analysis Research include R. W. L. Jones, Dumitru Bǎleanu and Jack M. Cuzick.

  1. 1 R. W. L. Jones United Kingdom 189k citations
  2. 2 Dumitru Bǎleanu Türkiye 89k citations
  3. 3 Jack M. Cuzick United Kingdom 80k citations

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

What are the most cited papers in Advanced Harmonic Analysis Research?

The most cited paper in Advanced Harmonic Analysis Research is "Hitchhikerʼs guide to the fractional Sobolev spaces" (Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci, 2011), with 4,369 citations. Next come "Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I" (3,784) and "Hp spaces of several variables" (2,887).

Most cited papers
#PaperReleasedCitations
1 Hitchhikerʼs guide to the fractional Sobolev spaces Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci · Bulletin des Sciences Mathématiques Open access 29 Dec 2011 4,369
2 Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I Shmuel Agmon, Avron Douglis, Louis Nirenberg · Communications on Pure and Applied Mathematics Nov 1959 3,784
3 Hp spaces of several variables Charles Fefferman, E. M. Stein · Acta Mathematica 1972 2,887
4 Endpoint Strichartz estimates M. Keel, Terence Tao · American Journal of Mathematics Oct 1998 2,081
5 Commutator estimates and the euler and navier‐stokes equations Tosio Kato, Gustavo Henrique Santos Flores Ponce · Communications on Pure and Applied Mathematics Oct 1988 1,919
All 100 most cited papers, with filters and sorting

Where is Advanced Harmonic Analysis Research research done?

The largest centres of Advanced Harmonic Analysis Research research in 2022-now are Beijing (China), Moscow (Russia), Guangzhou (China) and Changsha (China).

Largest cities, 2022-now

  1. 1 BeijingChina 91 works
  2. 2 MoscowRussia 43 works
  3. 3 GuangzhouChina 31 works
  4. 4 ChangshaChina 25 works
  5. 5 SeoulSouth Korea 24 works
  6. 6 BakuAzerbaijan 24 works
  7. 7 MadridSpain 23 works
  8. 8 WarsawPoland 23 works
  9. 9 HangzhouChina 22 works
  10. 10 TianjinChina 21 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, Beijing Normal University, Education University of Hong Kong and University of Jyväskylä 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 14.46%fractional works in this field (log) →share of work in the world top 10% →Beijing Normal Unive…Education University…University of Jyväsk…Ghent University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Beijing Normal UniversityChina 78.136.4%22.1×35 -4.8%
2Education University of Hong KongChina 71.136.3%44.5×13 -6.2%
3University of JyväskyläFinland 45.620.0%24.5×9 +91.7%
4Ghent UniversityBelgium 43.67.7%8.4×13 +47.8%
5United Arab Emirates UniversityUnited Arab Emirates 42.911.9%18.1×8 +64.4%
6Macquarie UniversityAustralia 41.810.0%14.5×10 +1.2%
7Xinjiang UniversityChina 39.25.1%21.0×18 +24.0%
8Zhejiang Normal UniversityChina 37.06.3%21.3×12 +72.2%
9Baylor UniversityUnited States 36.12.8%42.3×15 +193.2%
10Northwest Normal UniversityChina 34.58.1%27.5×13 +79.3%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Harmonic Analysis Research, country by country

Is Advanced Harmonic Analysis Research research growing?

Output in 2022-2025 was 10% higher than in 2018-2021, peaking in 2022. The fastest-growing topics are Advanced Harmonic Analysis Research.

still counting19801990200020102020
grewheldshrank

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

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Advanced Harmonic Analysis Research as a percentage of every work published that year, 0.0089% in 2024.

still counting0.010%0.020%Advanced Harmonic Analysis Research0.0086% in 202519801990200020102020

Fractional works of Advanced Harmonic Analysis Research over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Advanced Harmonic Analysis Research9.6% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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