Fractional integrals on spaces of homogeneous type

Vachtang Michailovič Kokilashvili; Alois Kufner

Commentationes Mathematicae Universitatis Carolinae (1989)

  • Volume: 030, Issue: 3, page 511-523
  • ISSN: 0010-2628

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Kokilashvili, Vachtang Michailovič, and Kufner, Alois. "Fractional integrals on spaces of homogeneous type." Commentationes Mathematicae Universitatis Carolinae 030.3 (1989): 511-523. <http://eudml.org/doc/17765>.

@article{Kokilashvili1989,
author = {Kokilashvili, Vachtang Michailovič, Kufner, Alois},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {fractional order integral; fractional maximal function},
language = {eng},
number = {3},
pages = {511-523},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fractional integrals on spaces of homogeneous type},
url = {http://eudml.org/doc/17765},
volume = {030},
year = {1989},
}

TY - JOUR
AU - Kokilashvili, Vachtang Michailovič
AU - Kufner, Alois
TI - Fractional integrals on spaces of homogeneous type
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1989
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 030
IS - 3
SP - 511
EP - 523
LA - eng
KW - fractional order integral; fractional maximal function
UR - http://eudml.org/doc/17765
ER -

References

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  3. Adams D., A trace inequality for generalized potentials, Studia Math. 48 (1973), 99-108. (1973) Zbl0237.46037MR0336316
  4. Coifman R., Weiss G., Analyse harmonique non-commutative sur certains espaces homogénes, Lecture Notes in Math. 242, Springer-Verlag, 1971. (1971) Zbl0224.43006MR0499948
  5. Kufner A., John O., Fučík S., Function spaces, Academia Prague. Noordhoff International Puhliahing, Leyden, 1977. (1977) MR0482102
  6. Stein E., Weiss G., Introduction to Fourier Analysis on Euclidian Spaces, Princeton University Press, Princeton, New Jersey, 1971. (1971) MR0304972
  7. Krasnosel'skii M. A., Rutickii Ya. B., Convex functions end Orlics spaces, Noordhoff, Groningen, 1961. (1961) 
  8. Musielak J., Modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, Berlin - Heidelberg - New York - Tokyo, 1983. (1983) Zbl0599.46036MR0724434
  9. Calderon A. P., Inequalities for the maximal function relative to a metric, Studia Math. 67 (1976), 297-306. (1976) Zbl0341.44007MR0442579
  10. Macias R. A., Segovia C., A well behaved quasi-distance for spaces of homogeneous type, Trab. Mat. Inst. Argent. Mat. 32 (1981), 18p. (1981) 
  11. Hedberg L., On certain convolution inequalities, Proc. Amer. Math. Soc 36 (1973), 505-610. (1973) Zbl0283.26003MR0312232
  12. Adams D., A note on Riesz potentials, Duke Math. J. 4 (1975), 765-777. (1975) Zbl0336.46038MR0458158
  13. O'Neil R., Les function conjugées et les intégrales fractionaires de la classe L ( l o g + L ) s , C.R. Acad. Sc. Paris 263 (1966), 463-466. (1966) 
  14. Welland G., Weighted norm inequalities for fractional integrals, Proc. Amer. Math. Soc. 61 (1975), 143-148. (1975) Zbl0306.26007MR0369641
  15. Kokilashvili V., Gabidsashvili M., Weighted inequalities for anisotropic potentials, (Russian). Dokl. Akad. Nauk. SSSR (1985), 1304-1306; English translation: Soviet Math. Dokl. 31 (1985), 583-585. (1985) 
  16. Kokilashvili V., Krbec M., On the boundedness of anisotropic fractional maximal functions and potentials in weighted Orlicz spaces, (Russian). Trudy Tbilias. Mat. Inst. Rasmadze Akad. Nauk Grusin. SSR 82 (1986), 106-115. (1986) MR0884700
  17. Genebashvili S., Two weight norm inequalities for fractional maximal functions defined on homogeneous type spaces, (Russian) Soobehch. Akad. Nauk Grusin SSR (to appear). 

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