The one-sided A p conditions and local maximal operator

We introduce the one-sided local maximal operator and study its connection to the one-sided Ap conditions. We get a new characterization of the boundedness of the one-sided maximal operator on a quasi-Banach function space. We obtain applications to weighted Lebesgue spaces and variable-exponent Lebesgue spaces.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; ArgentinaFil: Gogatishvili, Amiran. Institute Of Mathematics Of The Academy Of Sciences Of The Czech Republic; República ChecaFil: Martín Reyes, Francisco Javier. Universidad de Málaga; EspañaFil: Salvador, Pedro Ortega. Universidad de Málaga; EspañaFil: Pick, Luboš. Charles University; República Chec