Radial-Type Muckenhoupt Weights

  • Marilina Carena
  • Bibiana Iaffei
  • Marisa Toschi


Given a space of homogeneous type \((X,d,\mu )\) and \(1<p<\infty \), the main purpose of this note is to find sufficient conditions on a function w and on a subset F of X, such that w(d(xF)) belongs to the Muckenhoupt class \(A_p(X,d,\mu )\). Here d(xF) denotes the distance between \(x\in X\) and F.


Muckenhoupt weights Ahlfors spaces lower and upper indices 

Mathematics Subject Classification

42B25 47B38 


  1. 1.
    Aimar, H., Carena, M., Durán, R., Toschi, M.: Powers of distances to lower dimensional sets as Muckenhoupt weights. Acta Math. Hung. 143(1), 119–137 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Assouad, P.: Étude d’une dimension métrique liée à la possibilité de plongements dans \({ R}^{n}\). C. R. Acad. Sci. Paris Sér. A-B 288(15), A731–A734 (1979)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bricchi, M.: Existence and properties of \(h\)-sets. Georgian Math. J. 9(1), 13–32 (2002)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Coifman, R.R., Weiss, G.: Analyse harmonique non-commutative sur certains espaces homogènes. Lecture Notes in Mathematics, vol. 242. Springer, Berlin (1971)Google Scholar
  5. 5.
    García-Cuerva, J., de Francia, J.L.R.: Weighted norm inequalities and related topics, volume 116 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam (1985). Notas de Matemática [Mathematical Notes], 104Google Scholar
  6. 6.
    Karapetyants, N.K., Samko, N.: Weighted theorems on fractional integrals in the generalized Hölder spaces via indices \(m_\omega \) and \(M_\omega \). Fract. Calc. Appl. Anal. 7(4), 437–458 (2004)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Kokilashvili, V., Samko, S.: The maximal operator in weighted variable exponent spaces on metric spaces. Georgian Math. J. 15(4), 683–712 (2008)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Maligranda, L.: Indices and interpolation. Dissertationes Math. (Rozprawy Mat.) 234, 49 (1985)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Sjödin, T.: On \(s\)-sets and mutual absolute continuity of measures on homogeneous spaces. Manuscr. Math. 94(2), 169–186 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Departamento de Matemática (FHUC-UNL)Instituto de Matemática Aplicada del Litoral (CONICET-UNL)Santa FeArgentina

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