Fractional integrals on spaces of homogeneous type
Kokilashvili, Vachtang Michailovič ; Kufner, Alois
Commentationes Mathematicae Universitatis Carolinae, Tome 030 (1989), p. 511-523 / Harvested from Czech Digital Mathematics Library
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Publié le : 1989-01-01
Classification:  26A33,  42B25,  42B99,  43A15,  47B38,  47B99,  47G10 
@article{106773,
     author = {Vachtang Michailovi\v c Kokilashvili and Alois Kufner},
     title = {Fractional integrals on spaces of homogeneous type},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {030},
     year = {1989},
     pages = {511-523},
     zbl = {0686.42013},
     mrnumber = {1031869},
     language = {en},
     url = {http://dml.mathdoc.fr/item/106773}
}

Kokilashvili, Vachtang Michailovič; Kufner, Alois. Fractional integrals on spaces of homogeneous type. Commentationes Mathematicae Universitatis Carolinae, Tome 030 (1989) pp. 511-523. http://gdmltest.u-ga.fr/item/106773/

Sobolev S. L. On a theorem in functional analysis, (Russian). Mat. Sb. 4 (88) (1938), 471-497; (English translation: Amer. Math. Soc. Tranasl. 3 (84) (1983), 39-88). (1938)

Muckenhoupt B.; Wheeden R. L. Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 193 (1974), 281-274. (193 ) | MR 0340523

Adams D. A trace inequality for generalized potentials, Studia Math. 48 (1973), 99-108. (1973) | MR 0336316 | Zbl 0237.46037

Coifman R.; Weiss G. Analyse harmonique non-commutative sur certains espaces homogénes, Lecture Notes in Math. 242, Springer-Verlag, 1971. (1971) | MR 0499948 | Zbl 0224.43006

Kufner A.; John O.; Fučík S. Function spaces, Academia Prague. Noordhoff International Puhliahing, Leyden, 1977. (1977) | MR 0482102

Stein E.; Weiss G. Introduction to Fourier Analysis on Euclidian Spaces, Princeton University Press, Princeton, New Jersey, 1971. (1971) | MR 0304972

Krasnosel'Skii M. A.; Rutickii Ya. B. Convex functions end Orlics spaces, Noordhoff, Groningen, 1961. (1961)

Musielak J. Modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, Berlin - Heidelberg - New York - Tokyo, 1983. (1983) | MR 0724434 | Zbl 0599.46036

Calderon A. P. Inequalities for the maximal function relative to a metric, Studia Math. 67 (1976), 297-306. (1976) | MR 0442579 | Zbl 0341.44007

Macias R. A.; Segovia C. A well behaved quasi-distance for spaces of homogeneous type, Trab. Mat. Inst. Argent. Mat. 32 (1981), 18p. (1981)

Hedberg L. On certain convolution inequalities, Proc. Amer. Math. Soc 36 (1973), 505-610. (1973) | MR 0312232 | Zbl 0283.26003

Adams D. A note on Riesz potentials, Duke Math. J. 4 (1975), 765-777. (1975) | MR 0458158 | Zbl 0336.46038

O'Neil R. Les function conjugées et les intégrales fractionaires de la classe $L(log^+ L)^s$, C.R. Acad. Sc. Paris 263 (1966), 463-466. (1966)

Welland G. Weighted norm inequalities for fractional integrals, Proc. Amer. Math. Soc. 61 (1975), 143-148. (1975) | MR 0369641 | Zbl 0306.26007

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)

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) | MR 0884700

Genebashvili S. Two weight norm inequalities for fractional maximal functions defined on homogeneous type spaces, (Russian) Soobehch. Akad. Nauk Grusin SSR (to appear).