Potential operators associated with Jacobi and Fourier-Bessel expansions

  1. Nowak, A. 2
  2. Roncal, L 1
  1. 1 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  2. 2 Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, Warszawa, Poland
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Year of publication: 2015

Volume: 422

Issue: 1

Pages: 148-184

Type: Article

Export: RIS
DOI: 10.1016/j.jmaa.2014.08.023 SCOPUS: 2-s2.0-85027938886 WoS: 000349938500009 GOOGLE SCHOLAR
Institutional repository: lock_openOpen access editor


Cited by

  • Scopus Cited by: 12 (12-06-2021)

Journal Citation Reports

  • Year 2015
  • Journal Impact Factor: 1.014
  • Best Quartile: Q1
  • Area: MATHEMATICS Quartile: Q1 Rank in area: 56/312 (Ranking edition: SCIE)
  • Area: MATHEMATICS, APPLIED Quartile: Q2 Rank in area: 88/254 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2015
  • SJR Journal Impact: 1.15
  • Best Quartile: Q1
  • Area: Applied Mathematics Quartile: Q1 Rank in area: 100/545
  • Area: Analysis Quartile: Q2 Rank in area: 36/133


  • Year 2015
  • CiteScore of the Journal : 2.1
  • Area: Analysis Percentile: 74
  • Area: Applied Mathematics Percentile: 63


We study potential operators (Riesz and Bessel potentials) associated with classical Jacobi and Fourier-Bessel expansions. We prove sharp estimates for the corresponding potential kernels. Then we characterize those 1≤. p, q≤. ∞, for which the potential operators are of strong type (p, q), of weak type (p, q) and of restricted weak type (p, q). These results may be thought of as analogues of the celebrated Hardy-Littlewood-Sobolev fractional integration theorem in the Jacobi and Fourier-Bessel settings. As an ingredient of our line of reasoning, we also obtain sharp estimates of the Poisson kernel related to Fourier-Bessel expansions.