|
|||||
|
|
Alternative characterisations of Lorentz-Karamata spaces |
|
| Authors: | |
| Institution: | (1) School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4YH, England;(2) Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic;(3) Department of Mathematics and Didactics, Pedagogical Faculty, Technical University of Liberec, Hálkova 6, 461 17 Liberec, Czech Republic |
| Abstract: | 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. |
| Keywords: | Lorentz-Karamata spaces equivalent quasi-norms weighted norm inequalities fractional maximal operators Riesz potentials |
| 本文献已被 SpringerLink 等数据库收录！ | |