Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions

• Betancor, Jorge J. ^[1] ; Dalmasso, Estefanía ^[3] ; Quijano, Pablo ^[3] ; Scotto, Roberto ^[2]
  1. [1] Universidad de La Laguna

     Universidad de La Laguna

     San Cristóbal de La Laguna, España

     
  2. [2] Universidad Nacional del Litoral

     Universidad Nacional del Litoral

     Argentina

     
  3. [3] Instituto de Matemática Aplicada del Litoral, UNL, CONICET, FIQ, Colectora Ruta Nac. No 168, Paraje El Pozo, S3007ABA, Santa Fe, Argentina

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 2, 2025, págs. 303-336
• Idioma: inglés
• DOI: 10.1007/s13348-024-00433-z
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we introduce the atomic Hardy space \mathcal {H}^1((0,\infty ),\gamma _\alpha ) associated with the non-doubling probability measure d\gamma _\alpha (x)=\frac{2x^{2\alpha +1}}{\Gamma (\alpha +1)}e^{-x^2}dx on (0,\infty ), for {\alpha >-\frac{1}{2}}. We obtain characterizations of \mathcal {H}^1((0,\infty ),\gamma _\alpha ) by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from \mathcal {H}^1((0,\infty ),\gamma _\alpha ) into L^1((0,\infty ),\gamma _\alpha ).

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