| Title:
|
Norm inequalities in weighted amalgam (English) |
| Author:
|
Kumar, Suket |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
317-325 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Hardy inequalities for the Hardy-type operators are characterized in the amalgam space which involves Banach function space and sequence space. (English) |
| Keyword:
|
Hardy's inequality |
| Keyword:
|
amalgam space |
| Keyword:
|
weight function |
| MSC:
|
26D10 |
| MSC:
|
26D15 |
| idZBL:
|
Zbl 06940873 |
| idMR:
|
MR3861555 |
| DOI:
|
10.14712/1213-7243.2015.257 |
| . |
| Date available:
|
2018-09-10T12:10:03Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147400 |
| . |
| Reference:
|
[1] Bennett C., Sharpley R.: Interpolation of Operators.Pure and Applied Mathematics, 129, Academic Press, Boston, 1988. Zbl 0647.46057, MR 0928802 |
| Reference:
|
[2] Berezhnoĭ E. I.: Sharp estimates of operators on the cone of ideal spaces.Trudy Mat. Inst. Steklov. 204 (1993), Issled. po Teor. Differ. Funktsiĭ Mnogikh Peremen. i ee Prilozh. 16, 3–34 (Russian); translation in Proc. Steklov Inst. Math. 204 (1994), no. 3, 1–25. MR 1320016 |
| Reference:
|
[3] Carton-Lebrun C., Heinig H. P., Hofmann S. C.: Integral operators on weighted amalgams.Studia Math. 109 (1994), no. 2, 133–157. MR 1269772, 10.4064/sm-109-2-133-157 |
| Reference:
|
[4] Fournier J. J. F., Stewart J.: Amalgams of $L^p$ and $\ell^q$.Bull. Amer. Math. Soc. (N.S.) 13 (1985), no. 1, 1–21. MR 0788385, 10.1090/S0273-0979-1985-15350-9 |
| Reference:
|
[5] Jain P., Kumar S.: Weighted inequalities of Hardy-type on amalgams.Real Anal. Exchange 34 (2008/2009), no. 2, 483–499. MR 2569200, 10.14321/realanalexch.34.2.0483 |
| Reference:
|
[6] Jain P., Kumar S.: Boundedness of Hardy operators on generalized amalgams.Math. Inequal. Appl. 12 (2009 ), no. 3, 549–562. MR 2540978 |
| Reference:
|
[7] Kufner A., Persson L.-E.: Weighted Inequalities of Hardy Type.World Scientific Publishing, River Edge, 2003. Zbl 1065.26018, MR 1982932 |
| Reference:
|
[8] Lomakina E., Stepanov V.: On the Hardy-type integral operators in Banach function spaces.Publ. Mat. 42 (1998), no. 1, 165–194. MR 1628166, 10.5565/PUBLMAT_42198_09 |
| Reference:
|
[9] Luxemburg W. A. J.: Banach Function Spaces.Ph.D. Thesis, Delft Institute of Technology, Aseen, 1955. Zbl 0162.44701, MR 0072440 |
| Reference:
|
[10] Salvador P. O., Torreblanca C. R.: Hardy operators on weighted amalgams.Proc. Royal Soc. Edinburgh, Section A 140 (2010), no. 1, 175–188. MR 2592719 |
| Reference:
|
[11] Wiener N.: On the representation of functions by trigonometrical integrals.Math. Z. 24 (1926), no. 1, 575–616. MR 1544780, 10.1007/BF01216799 |
| Reference:
|
[12] Zharov P. A.: On a two-weight inequality. Generalization of Hardy and Poincaré inequalities.Trudy Mat. Inst. Steklov. 194 (1992), Issled. po Teor. Differ. Funktsiĭ Mnogikh Peremen. i ee Prilozh. 14, 97–110 (Russian); translation in Proc. Steklov Inst. Math. 194 (1993), no. 4, 101–114. MR 1289650 |
| . |
