| Title:
|
On conditions for the boundedness of the Weyl fractional integral on weighted $L^p$ spaces (English) |
| Author:
|
de Rosa, L. |
| Author:
|
de la Torre, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
17-36 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we give a sufficient condition on the pair of weights $(w,v)$ for the boundedness of the Weyl fractional integral $I_{\alpha}^+$ from $L^p(v)$ into $L^p(w)$. Under some restrictions on $w$ and $v$, this condition is also necessary. Besides, it allows us to show that for any $p: 1 \leq p < \infty $ there exist non-trivial weights $w$ such that $I_{\alpha}^+$ is bounded from $L^p(w)$ into itself, even in the case $\alpha > 1$. (English) |
| Keyword:
|
Weyl fractional integrals |
| Keyword:
|
weights |
| MSC:
|
26A33 |
| MSC:
|
42B25 |
| MSC:
|
44A15 |
| idZBL:
|
Zbl 1100.26003 |
| idMR:
|
MR2076858 |
| . |
| Date available:
|
2009-05-05T16:43:07Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119435 |
| . |
| Reference:
|
[1] Bennett C., Sharpley R.: Interpolation of Operators.Academic Press, 1988. Zbl 0647.46057, MR 0928802 |
| Reference:
|
[2] García-Cuerva J., Rubio de Francia J.L.: Weighted Norm Inequalities and Related Topics.North-Holland, 1985. MR 0848147 |
| Reference:
|
[3] Hernández e.: Weighted inequalities through factorization.Publ. Mat. 35 (1991), 141-153. MR 1103612 |
| Reference:
|
[4] Lorente M., de la Torre A.: Weighted inequalities for some one-sided operators.Proc. Amer. Math. Soc. 124 (1996), 839-848. Zbl 0895.26002, MR 1317510 |
| Reference:
|
[5] Martín Reyes F.J., Sawyer E.: Weighted inequalities for Riemann-Liouville fractional integrals of order one and greater.Proc. Amer. Math. Soc. 106 (3) (1989), 727-733. MR 0965246 |
| Reference:
|
[6] Verbitsky I.E., Wheeden R.L.: Weighted trace inequalities for fractional integrals and applications to semilinear equations.J. Funct. Anal. 129 (1) (1995), 221-241. Zbl 0830.46029, MR 1322649 |
| . |
