Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements

• Autores: Fritz Gesztesy, Isaac Michael, Michael M. H. Pang
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 1, 2022, págs. 115-165
• Idioma: inglés
• DOI: 10.4067/S0719-06462022000100115
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• Resumen
  • español

    RESUMEN El objetivo principal de este artículo es establecer la optimalidad (i.e. la precisión) de las constantes A(m, α) y B(m, α), m ∈ ℕ, α ∈ ℝ, de la forma en las desigualdades integrales de tipo Birman-Hardy-Rellich pesadas por potencias con términos de refinamiento logarítmicos recientemente demostradas en [41], es decir, Acá los logaritmos iterados están dados por y las exponenciales iteradas están definidas por Más aún, probamos la secuencia análoga de desigualdades en el intervalo exterior (r,∞) para f ∈ C ∞ 0 ((r,∞)), r ∈ (0, ∞), y una vez más probamos la optimalidad de las constantes involucradas.

  • English

    ABSTRACT The principal aim of this paper is to establish the optimality (i.e., sharpness) of the constants A(m, α) and B(m, α), m ∈ ℕ, α ∈ ℝ, of the form in the power-weighted Birman-Hardy-Rellich-type integral inequalities with logarithmic refinement terms recently proved in [41], namely, Here the iterated logarithms are given by and the iterated exponentials are defined via Moreover, we prove the analogous sequence of inequalities on the exterior interval (r,∞) for f ∈ C ∞ 0 ((r,∞)), r ∈ (0, ∞), and once again prove optimality of the constants involved.

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