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Compactness of Fractional Type Integral Operators on Spaces of Homogeneous Type

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For a space (X, d, μ) of homogeneous type and a fractional type integral operator Kα defined on (X, d, μ) we find a necessary and sufficient condition on the exponent q governing the compactness of Kα from Lp(X) to Lq(X), where 1 ≤ p, q < ∞ and μ(X) < ∞.

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References

  1. D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Springer, Berlin (1996).

    Book  MATH  Google Scholar 

  2. V. G. Maz’ya, Sobolev Spaces, Springer, Berlin (1985).

    Book  MATH  Google Scholar 

  3. M. A. Kransnoselskii, P. P. Zabreiko, E. I. Pustylnik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions, Noordhoft, Leiden (1976).

    Book  Google Scholar 

  4. V. Kokilashvili, M. Mastylo, and A. Meskhi, “Compactness criteria for fractional integral operators,” Fract. Calc. Appl. Anal. 22, No. 5, 1259–1283 (2019).

  5. V. Kokilashvili and A. Meskhi, “Fractional integrals on measure spaces,” Fract. Calc. Appl. Anal. 4, No. 1, 1–24 (2001).

    MathSciNet  MATH  Google Scholar 

  6. V. Kokilashvili, “Weighted estimates for classical integral operators,” Teubner-Texte Math. 119, 86–103 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  7. R. A. Macías and C. Segovia, “Lipschitz functions on spaces of homogeneous type,” Adv. Math. 33, 257–270 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  8. R. R. Coifman and G. Weiss, “Analyse harmonique non-commutative sur certains espaces homogenes,” Lect. Notes Math. 242, (1971).

  9. G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups Princeton Univ. Press, Princeton. NJ (1982).

  10. J.-O. Strömberg and A. Torchinsky, “Weighted Hardy spaces,” Lect. Notes Math. 1381 (1989).

  11. A. Grothendieck, “Sur les applications linéaires faiblement compactes d’espaces du type C(K),” Can. J. Math. 5, 129–173 (1953).

    Article  MATH  Google Scholar 

  12. T. Andô, “On compactness of integral operators,” Nederl. Akad. Wet., Proc., Ser. A 24, 235–239 (1962).

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2, Merab Aleksidze II Lane, 0193, Tbilisi, Georgia

    V. Kokilashvili & A. Meskhi

  2. School of Mathematics, Kutaisi International University, 5th Lane, K Building, 4600, Kutaisi, Georgia

    A. Meskhi

Authors
  1. V. Kokilashvili
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  2. A. Meskhi
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Correspondence to A. Meskhi.

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Dedicated to the 85th birthday of Professor V. Maz’ya

Translated from Problemy Matematicheskogo Analiza 118, 2022, pp. 109-115.

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Kokilashvili, V., Meskhi, A. Compactness of Fractional Type Integral Operators on Spaces of Homogeneous Type. J Math Sci 268, 368–375 (2022). https://doi.org/10.1007/s10958-022-06202-2

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  • DOI: https://doi.org/10.1007/s10958-022-06202-2

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