Weighted modular estimates for a generalized maximal operator on spaces of homogeneous type

• Autores: Ana María Kanashiro, Gladis Pradolini, Oscar Salinas
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 63, Fasc. 2, 2012, págs. 147-164
• Idioma: inglés
• DOI: 10.1007/s13348-010-0027-3
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study weighted modular inequalities for a generalized maximal operator associated to a Young function in the context of spaces of homogeneous type. We prove the equivalence between these inequalities and a Dini-type condition, which involves the function associated to the operator and the functions related to the modular estimates. Particularly we obtain a generalization of a result of Perez and Wheeden (J Funct Anal 181(1):146–188, 2001). In addition we prove a characterization of the A 1-Muckenhoupt class, that extends and improves the corresponding results proved by Kita (Acta Math Hungar 72(4):291–305, 1996; Math Nachr 178:1180–1189, 2005).

• Referencias bibliográficas
  • Aimar H.: Singular integrals and approximate identities on spaces of homogeneous type. Trans. Am. Math. Soc. 292(1), 135–153 (1985)
  • Bagby R.: Weak bounds for the maximal function in weighted Orlicz spaces. Stud. Math. 95, 195–204 (1990)
  • Bernardis A., Hartzstein S., Pradolini G.: Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type. J....
  • Bernardis A., Salinas O.: Two-weight inequalities for certain maximal fractional operators on spaces of homogeneous type. Revista de la Unión...
  • Coifman, R., Weiss, G.: Analyse harmonique non-commutative sur certains espaces homogènes. In: Lecture Notes in Mathematics, vol. 242. Springer-Verlag,...
  • Harboure E., Salinas O., Viviani B.: Orlicz boundedness for certain classical operators. Colloq. Math. 91(2), 263–282 (2002)
  • Kita H.: On maximal functions in Orlicz spaces. Proc. Am. Math. Soc. 124, 3019–3025 (1996)
  • Kita H.: Weighted inequalities for iterated maximal functions in Orlicz spaces. Math. Nachr. 178, 1180–1189 (2005)
  • Kita H.: Inequalities with weights for maximal functions in Orlicz spaces. Acta Math. Hungar. 72(4), 291–305 (1996)
  • Macías R., Segovia C.: Lipschitz functions on spaces of homogeneous type. Adv. Math. 33, 257–270 (1979)
  • Macías R., Segovia C.: Singular integrals on generalized Lipschitz and Hardy spaces. Stud. Math. 65, 55–75 (1979)
  • Macías R., Segovia C., Torrea J.: Singular integrals operators with non-necessarily bounded kernels on spaces of homogeneous type. Adv. Math....
  • Pérez C.: On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted L p spaces with different...
  • Pérez C., Wheeden R.: Uncertainty principle estimates for vector fields. J. Funct. Anal. 181(1), 146–188 (2001)
  • Pradolini G., Salinas O.: Maximal operators on spaces of homogeneous type. Proc. Am. Math. Soc. 132(2), 435–441 (2003)
  • Rao M., Ren Z.: Theory of Orlicz Spaces. Marcel Dekker, New York (1991)