The Calderón operator and the Stieltjes transform on variable Lebesgue spaces with weights

• Autores: David Cruz-Uribe , Estefanía Dalmasso, Francisco Javier Martín Reyes , Pedro Ortega Salvador
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 3, 2020, págs. 443-469
• Idioma: inglés
• DOI: 10.1007/s13348-019-00272-3
• Texto completo no disponible (Saber más ...)
• Resumen

  • We characterize the weights for the Stieltjes transform and the Calderón operator to be bounded on the weighted variable Lebesgue spaces L_w^{p(\cdot )}(0,\infty ), assuming that the exponent function {p(\cdot )} is log-Hölder continuous at the origin and at infinity. We obtain a single Muckenhoupt-type condition by means of a maximal operator defined with respect to the basis of intervals \{ (0,b) : b>0\} on (0,\infty ). Our results extend those in Duoandikoetxea et al. (Indiana Univ Math J 62(3):891–910, 2013) for the constant exponent L^p spaces with weights. We also give two applications: the first is a weighted version of Hilbert’s inequality on variable Lebesgue spaces, and the second generalizes the results in Soria and Weiss (Indiana Univ Math J 43(1):187–204, 1994) for integral operators to the variable exponent setting.

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