Applications of generalized perron trees to maximal functions and density bases |
| |
Authors: | Kathryn E. Hare Jan-Olav Rönning |
| |
Affiliation: | 1. Department of Pure mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada 2. Institutionen f?r Naturvetenskap, H?gskolan i Sk?vde, Box 406, 541 28, Sk?vde, Sweden
|
| |
Abstract: | In this article we give some new necessary conditions for subsets of the unit circle to give collections of rectangles (by means of orientations) which differentiate Lp-functions or give Hardy-Littlewood type maximal functions which are bounded on Lp, p>1. This is done by proving that a well-known method, the construction of a Perron Tree, can be applied to a larger collection of subsets of the unit circle than was earlier known. As applications, we prove a partial converse of a well-known result of Nagel et al. [6] regarding boundedness of maximal functions with respect to rectangles of lacunary directions, and prove a result regarding the cardinality of subsets of arithmetic progressions in sets of the type described above. Acknowledgements and Notes. This research was partially supported by NSERC. |
| |
Keywords: | Primary: 42B25 |
本文献已被 SpringerLink 等数据库收录! |
|