Weighted Hardy and singular operators in Morrey spaces |
| |
Authors: | Natasha Samko |
| |
Institution: | Universidade do Algarve, Departamento de Matemática, Campus de Gambelas, Gambelas 8005-139, Faro, Portugal |
| |
Abstract: | We study the weighted boundedness of the Cauchy singular integral operator SΓ in Morrey spaces Lp,λ(Γ) on curves satisfying the arc-chord condition, for a class of “radial type” almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces Lp,λ(0,?), ?>0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves. |
| |
Keywords: | Morrey space Singular operator Hardy operator Hardy-Littlewood maximal operator Weighted estimate |
本文献已被 ScienceDirect 等数据库收录! |
|