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Radial-Type Muckenhoupt Weights

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Abstract

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(x, F)) belongs to the Muckenhoupt class \(A_p(X,d,\mu )\). Here d(x, F) denotes the distance between \(x\in X\) and F.

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References

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  3. Bricchi, M.: Existence and properties of \(h\)-sets. Georgian Math. J. 9(1), 13–32 (2002)

    MathSciNet  MATH  Google Scholar 

  4. Coifman, R.R., Weiss, G.: Analyse harmonique non-commutative sur certains espaces homogènes. Lecture Notes in Mathematics, vol. 242. Springer, Berlin (1971)

  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], 104

  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)

    MathSciNet  MATH  Google Scholar 

  7. Kokilashvili, V., Samko, S.: The maximal operator in weighted variable exponent spaces on metric spaces. Georgian Math. J. 15(4), 683–712 (2008)

    MathSciNet  MATH  Google Scholar 

  8. Maligranda, L.: Indices and interpolation. Dissertationes Math. (Rozprawy Mat.) 234, 49 (1985)

    MathSciNet  MATH  Google Scholar 

  9. Sjödin, T.: On \(s\)-sets and mutual absolute continuity of measures on homogeneous spaces. Manuscr. Math. 94(2), 169–186 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    Marilina Carena, Bibiana Iaffei & Marisa Toschi

Authors
  1. Marilina Carena
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  2. Bibiana Iaffei
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  3. Marisa Toschi
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Correspondence to Marisa Toschi.

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Carena, M., Iaffei, B. & Toschi, M. Radial-Type Muckenhoupt Weights. Mediterr. J. Math. 14, 50 (2017). https://doi.org/10.1007/s00009-017-0869-y

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  • DOI: https://doi.org/10.1007/s00009-017-0869-y

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