| Title:
|
The fractional integral between weighted Orlicz and $BMO_{\phi}$ spaces on spaces of homogeneous type (English) |
| Author:
|
Pradolini, Gladis |
| Author:
|
Salinas, Oscar |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
469-487 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable $BMO_{\phi}$ spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted $L^{p}$ and Lipschitz integral spaces on $\Bbb R^n$. We also give some properties of the classes of pairs of weights appearing in connection with this boundedness. (English) |
| Keyword:
|
weights |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
$BMO$ |
| Keyword:
|
fractional integral |
| MSC:
|
26A33 |
| MSC:
|
42B25 |
| MSC:
|
46E30 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 1103.46019 |
| idMR:
|
MR2025814 |
| . |
| Date available:
|
2009-01-08T19:30:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119402 |
| . |
| Reference:
|
[BS] Bernardis A., Salinas O.: Two-weighted inequalities for certain maximal fractional operators on spaces of homogeneous type.Revista de la Unión Matemática Argentina 41 3 (1999). MR 1763261 |
| Reference:
|
[GGKK] Genebashvili I., Gogatishvili A., Kokilashvili V., Krbec M.: Weight Theory for Integral Transforms on Spaces of Homogeneous Type.Addison Wesley Longman Limited, Harlow, 1998. Zbl 0955.42001, MR 1791462 |
| Reference:
|
[GV] Gatto A., Vagi S.: Fractional integrals on spaces of homogeneous type.Analysis and Partial Differential Equations, Lecture Notes in Pure and Appl. Math., Vol. 122, Marcel Dekker, New York, 1990, pp.171-216. Zbl 1002.42501, MR 1044788 |
| Reference:
|
[HSV1] Harboure E., Salinas O., Viviani B.: Boundedness of the fractional integral on weighted Lebesgue spaces and Lipschitz spaces.Trans. Amer. Math. Soc. 349 1 (1997), 235-255. MR 1357395 |
| Reference:
|
[HSV2] Harboure E., Salinas O., Viviani B.: Relations between weighted Orlicz and $BMO(\phi)$ spaces through fractional integrals.Comment. Math. Univ. Carolinae 40 1 (1999), 53-69. MR 1715202 |
| Reference:
|
[KK] Kokilashvili V., Krbec M.: Weighted Inequalities in Lorentz and Orlicz Spaces.World Scientific, River Edge, NJ, 1991. Zbl 0751.46021, MR 1156767 |
| Reference:
|
[MST] Macías R., Segovia C., Torrea J.: Singular integral operators with non-necessarily bounded kernels on spaces of homogeneous type.Adv. Math. 93 1 (1992). MR 1160842 |
| Reference:
|
[MT] Macías R., Torrea J.: $L^{2}$ and $L^p$ boundedness of singular integrals on non necessarily normalized spaces of homogeneous type.Cuadernos de Matemática y Mecánica, No. 1-88, PEMA-INTEC-GTM, Santa Fe, Argentina. |
| Reference:
|
[MW] Muckenhoupt B., Wheeden R.: Weighted norm inequalities for the fractional integrals.Trans. Amer. Math. Soc. 192 261-274 (1974). MR 0340523 |
| Reference:
|
[P1] Pradolini G.: Two-weighted norm inequalities for the fractional integral operator between $L^p$ and Lipschitz spaces.Comment. Math. Prace Mat. 41 (2001), 147-169. MR 1876717 |
| Reference:
|
[P2] Pradolini G.: A class of pairs of weights related to the boundedness of the Fractional Integral Operator between $L^p$ and Lipschitz spaces.Comment. Math. Univ. Carolinae 42 (2001), 133-152. MR 1825378 |
| Reference:
|
[RR] Rao, M.M., Ren Z.D.: Theory of Orlicz Spaces.Marcel Dekker, New York, 1991. Zbl 0724.46032, MR 1113700 |
| Reference:
|
[S] Sawyer E.: A characterization of two-weight norm inequalities related to the fractional and Poisson integrals.Trans. Amer. Math. Soc. 308 533-545 (1988). MR 0930072 |
| . |
