| Title:
|
Dual spaces of local Morrey-type spaces (English) |
| Author:
|
Gogatishvili, Amiran |
| Author:
|
Mustafayev, Rza |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
609-622 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities. (English) |
| Keyword:
|
local Morrey-type spaces |
| Keyword:
|
complementary local Morrey-type spaces |
| Keyword:
|
associated spaces |
| Keyword:
|
dual spaces |
| Keyword:
|
multidimensional reverse Hardy inequalities |
| MSC:
|
26D15 |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 1249.46020 |
| idMR:
|
MR2853078 |
| DOI:
|
10.1007/s10587-011-0034-x |
| . |
| Date available:
|
2011-09-22T14:29:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141625 |
| . |
| Reference:
|
[1] Burenkov, V. I., Guliyev, H. V.: Necessary and sufficient conditions for boundedness of the maximal operator in the local Morrey-type spaces.Stud. Math. 163 (2004), 157-176. MR 2047377, 10.4064/sm163-2-4 |
| Reference:
|
[2] Burenkov, V. I., Guliyev, H. V., Guliyev, V. S.: On boundedness of the fractional maximal operator from complementary Morrey-type spaces to Morrey-type spaces.The Interaction of Analysis and Geometry. International School-Conference on Analysis and Geometry, Novosibirsk, Russia, August 23--September 3, 2004 American Mathematical Society (AMS) Providence Contemporary Mathematics 424 (2007), 17-32. MR 2316329 |
| Reference:
|
[3] Burenkov, V. I., Guliyev, H. V., Guliyev, V. S.: Necessary and sufficient conditions for boundedness of fractional maximal operators in local Morrey-type spaces.J. Comput. Appl. Math. 208 (2007), 280-301. MR 2347750, 10.1016/j.cam.2006.10.085 |
| Reference:
|
[4] Burenkov, V. I., Guliyev, H. V., Tararykova, T. V., Serbetci, A.: Necessary and sufficient conditions for the boundedness of genuine singular integral operators in the local Morrey-type spaces.Dokl. Math. 78 (2008), 651-654 Translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 422 (2008), 11-14. MR 2475077, 10.1134/S1064562408050025 |
| Reference:
|
[5] Burenkov, V. I., Guliyev, V. S.: Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces.Potential Anal. 30 (2009), 211-249. Zbl 1171.42003, MR 2480959, 10.1007/s11118-008-9113-5 |
| Reference:
|
[6] Burenkov, V. I., Gogatishvili, A., Guliyev, V. S., Mustafayev, R. Ch.: Boundedness of the fractional maximal operator in Morrey-type spaces.Complex Var. Elliptic Equ. 55 (2010), 739-758. MR 2674862 |
| Reference:
|
[7] Evans, W. D., Gogatishvili, A., Opic, B.: The reverse Hardy inequality with measures.Math. Inequal. Appl. 11 (2008), 43-74. Zbl 1136.26004, MR 2376257 |
| Reference:
|
[8] Gogatishvili, A., Mustafayev, R.: The multidimensional reverse Hardy inequalities.Math. Inequal. & Appl. 14 (2011) (to appear) Preprint, Institute of Mathematics, AS CR, Prague 2009-5-27. Available at http://www.math.cas.cz/preprint/pre-179.pdf. MR 2853078 |
| Reference:
|
[9] Guliyev, V. S.: Integral operators on function spaces on the homogeneous groups and on domains in $\Bbb R^n$.Doctor's degree dissertation Mat. Inst. Steklov Moscow (1994), Russian. |
| Reference:
|
[10] Guliyev, V. S.: Function Spaces, Integral Operators and Two Weighted Inequalities on Homogeneous Groups. Some Applications.Baku (1999), Russian. |
| Reference:
|
[11] Guliyev, V. S., Mustafayev, R. Ch.: Integral operators of potential type in spaces of homogeneous type.Dokl. Math. 55 (1997), 427-429 Translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 354 (1997), 730-732. MR 1473130 |
| Reference:
|
[12] Guliyev, V. S., Mustafayev, R. Ch.: Fractional integrals on spaces of homogeneous type.Anal. Math. 24 (1998), 1810-200 Russian. |
| . |
