Maximal Operators and Cantor Sets

Canadian mathematical bulletin

关键词: maximal functions;    Cantor set;    lacunary set;   

DOI  :  10.4153/CMB-2000-040-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We consider maximal operators in the plane, defined by Cantor sets ofdirections, and show such operators are not bounded on $L^2$ if theCantor set has positive Hausdorff dimension.

【 授权许可】

Unknown