Journals / Turkish Journal of Mathematics / 2006 / Cilt: 30 - Sayı: 4
Weighted Norm Inequalities for a Class of Rough Maximal Operators
- Pages
- 413–438
- DOI
- —
Abstract
We consider maximal singular integral operators arising from rough kernels satisfying an H1-type condition on the unit (n-1)-sphere and prove weighted Lp estimates for certain radial weights. We also prove weighted Lp estimates with Ap-weights where in this case the H1 -type condition is replaced by an Lq-type condition with q > 1. Some applications of these results are also obtained regarding singular integrals and Marcinkiewicz integrals. Our results are essential extensions and improvements of some known results.
Özet
We consider maximal singular integral operators arising from rough kernels satisfying an H1-type condition on the unit (n-1)-sphere and prove weighted Lp estimates for certain radial weights. We also prove weighted Lp estimates with Ap-weights where in this case the H1 -type condition is replaced by an Lq-type condition with q > 1. Some applications of these results are also obtained regarding singular integrals and Marcinkiewicz integrals. Our results are essential extensions and improvements of some known results.