Restricted weak type inequalities for convolution maximal operators in weighted Lp spaces

• Autores: Bernardis, Ana Lucia; Martín Reyes, Francisco Javier
• Año de publicación: 2003
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Restricted weak; Maximal operators; Weighted Lp spaces
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

Let φ: ℝ → [0, ∞) be an integrable function such that φ(-∞,0) = 0 and φ is decreasing in (0, ∞). Let τh f (x) = f (x - h), with h ∈ ℝ/{0} and φ R(x) = (1/R)φ(x/R), with R > 0. In this paper we study the pair of weights (u, v) such that the operators Mτhφ f (x) = supR>0 |f| * [tau;hφ]R (x) are of restricted weak type (p, p) with respect to (u, v), 1 ≤ p < ∞. As particular cases, these operators include some maximal operators related to Cesàro convergence. We characterize those functions φ for which Mτhφ is of (restricted) weak type (p, p) with respect to the Lebesgue measure. Unlike the case of the Cesàro maximal operators, it follows from the characterization that the interval of those p such that M τhφ is of weak type (p, p) can be left-closed, [p 0, ∞], or left-open, (p0, ∞], without having restricted weak type (p0, p0).
Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Martín Reyes, Francisco Javier. Universidad de Málaga; España