| Title:
|
A two weight weak inequality for potential type operators (English) |
| Author:
|
Kokilashvili, Vachtang |
| Author:
|
Rákosník, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
251-263 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give conditions on pairs of weights which are necessary and sufficient for the operator $T(f)=K\ast f$ to be a weak type mapping of one weighted Lorentz space in another one. The kernel $K$ is an anisotropic radial decreasing function. (English) |
| Keyword:
|
integral operator |
| Keyword:
|
anisotropic potential |
| Keyword:
|
weighted Lorentz space |
| MSC:
|
31B15 |
| MSC:
|
42B20 |
| MSC:
|
46E30 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 0746.42011 |
| idMR:
|
MR1137786 |
| . |
| Date available:
|
2008-10-09T13:12:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116963 |
| . |
| Reference:
|
[1] Chang H.M., Hunt R.A., Kurtz D.S.: The Hardy-Littlewood maximal function on $L(p,q)$ spaces with weight.Indiana Univ. Math. J. 31 (1982), no.1, 109-120. MR 0642621 |
| Reference:
|
[2] Gabidzashvili M.: Weighted inequalities for anisotropic potentials.Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 82 (1986), 25-36. MR 0884696 |
| Reference:
|
[3] Gabidzashvili M., Genebashvili J., Kokilashvili V.: Two weight inequalities for generalized potentials (in Russian).Trudy Mat. Inst. Steklov, to appear. MR 1221297 |
| Reference:
|
[4] Kokilashvili V.: Weighted inequalities for maximal functions and fractional integrals in Lorentz spaces.Math. Nachr. 133 (1987), 33-42. Zbl 0652.42005, MR 0912418 |
| Reference:
|
[5] Kokilashvili V., Gabidzashvili M.: Weighted inequalities for anisotropic potentials and maximal functions (in Russian).Dokl. Akad. Nauk SSSR 282 (1985), no. 6, 1304-1306 English translation: Soviet Math. Dokl. 31 (1985), no. 3, 583-585. MR 0802694 |
| Reference:
|
[6] Kokilashvili V., Gabidzashvili M.: Two weight weak type inequalities for fractional type integrals.preprint no. 45, Mathematical Institute of the Czechoslovak Academy of Sciences, Prague 1989. |
| Reference:
|
[7] Sawyer E.T.: A two weight type inequality for fractional integrals.Trans. Amer. Math. Soc. 281 (1984), no. 1, 339-345. MR 0719674 |
| . |
