| Title:
|
Alternative characterisations of Lorentz-Karamata spaces (English) |
| Author:
|
Edmunds, D. E. |
| Author:
|
Opic, B. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
517-540 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces. (English) |
| Keyword:
|
Lorentz-Karamata spaces |
| Keyword:
|
equivalent quasi-norms |
| Keyword:
|
weighted norm inequalities |
| Keyword:
|
fractional maximal operators |
| Keyword:
|
Riesz potentials |
| MSC:
|
26D10 |
| MSC:
|
42B35 |
| MSC:
|
46E30 |
| MSC:
|
47B38 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 1174.46019 |
| idMR:
|
MR2411107 |
| . |
| Date available:
|
2009-09-24T11:56:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128275 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[15] B. Opic: On equivalent quasi-norms on Lorentz spaces.In Function Spaces, Differential Operators and Nonlinear Analysis. The Hans Triebel Aniversary Volume, D. Haroske, T. Runst, H.-J. Schmeisser (eds.), Birkhäuser Verlag, Basel/Switzerland, 2003, pp. 415–426. Zbl 1036.46022, MR 1984189 |
| Reference:
|
[16] B. Opic and W. Trebels: Sharp embeddings of Bessel potential spaces with logarithmic smoothness.Math. Proc. Camb. Phil. Soc. 134 (2003), 347–384. MR 1972143, 10.1017/S0305004102006321 |
| . |
