| Title:
|
Fractional integrals on spaces of homogeneous type (English) |
| Author:
|
Kokilashvili, Vakhtang M. |
| Author:
|
Kufner, Alois |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1989 |
| Pages:
|
511-523 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A33 |
| MSC:
|
42B25 |
| MSC:
|
42B99 |
| MSC:
|
43A15 |
| MSC:
|
47B38 |
| MSC:
|
47B99 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 0686.42013 |
| idMR:
|
MR1031869 |
| . |
| Date available:
|
2008-06-05T21:39:52Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106773 |
| . |
| Reference:
|
[1] 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). |
| Reference:
|
[2] Muckenhoupt B., Wheeden R. L.: Weighted norm inequalities for fractional integrals.Trans. Amer. Math. Soc. 193 (1974), 281-274. MR 0340523 |
| Reference:
|
[3] Adams D.: A trace inequality for generalized potentials.Studia Math. 48 (1973), 99-108. Zbl 0237.46037, MR 0336316 |
| Reference:
|
[4] Coifman R., Weiss G.: Analyse harmonique non-commutative sur certains espaces homogénes.Lecture Notes in Math. 242, Springer-Verlag, 1971. Zbl 0224.43006, MR 0499948 |
| Reference:
|
[5] Kufner A., John O., Fučík S.: Function spaces.Academia Prague. Noordhoff International Puhliahing, Leyden, 1977. MR 0482102 |
| Reference:
|
[8] Stein E., Weiss G.: Introduction to Fourier Analysis on Euclidian Spaces.Princeton University Press, Princeton, New Jersey, 1971. MR 0304972 |
| Reference:
|
[7] Krasnosel'skii M. A., Rutickii Ya. B.: Convex functions end Orlics spaces.Noordhoff, Groningen, 1961. |
| Reference:
|
[8] Musielak J.: Modular spaces.Lecture Notes in Math. 1034, Springer-Verlag, Berlin - Heidelberg - New York - Tokyo, 1983. Zbl 0599.46036, MR 0724434 |
| Reference:
|
[9] Calderon A. P.: Inequalities for the maximal function relative to a metric.Studia Math. 67 (1976), 297-306. Zbl 0341.44007, MR 0442579 |
| Reference:
|
[10] Macias R. A., Segovia C.: A well behaved quasi-distance for spaces of homogeneous type.Trab. Mat. Inst. Argent. Mat. 32 (1981), 18p. |
| Reference:
|
[11] Hedberg L.: On certain convolution inequalities.Proc. Amer. Math. Soc 36 (1973), 505-610. Zbl 0283.26003, MR 0312232 |
| Reference:
|
[12] Adams D.: A note on Riesz potentials.Duke Math. J. 4 (1975), 765-777. Zbl 0336.46038, MR 0458158 |
| Reference:
|
[13] 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. |
| Reference:
|
[14] Welland G.: Weighted norm inequalities for fractional integrals.Proc. Amer. Math. Soc. 61 (1975), 143-148. Zbl 0306.26007, MR 0369641 |
| Reference:
|
[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. |
| Reference:
|
[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. MR 0884700 |
| Reference:
|
[17] Genebashvili S.: Two weight norm inequalities for fractional maximal functions defined on homogeneous type spaces.(Russian) Soobehch. Akad. Nauk Grusin SSR (to appear). |
| . |
