Potential operators associated with Jacobi and Fourier-Bessel expansions

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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

ISSN: 0022-247X

Any de publicació: 2015

Volum: 422

Número: 1

Pàgines: 148-184

Tipus: Article

DOI: 10.1016/J.JMAA.2014.08.023 SCOPUS: 2-s2.0-85027938886 WoS: WOS:000349938500009 GOOGLE SCHOLAR

Altres publicacions en: Journal of Mathematical Analysis and Applications

Repositori institucional: lockAccés obert Editor

Projectes relacionats

Ortogonalidad y aproximación: teoría y aplicaciones en ciencia y tecnología

2013/00004/001

Resum

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.