Kathryn E. Hare
Abstract
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Abstract We consider maximal operators in the plane, defined by Cantor sets of directions, and show such operators are not bounded on L2 if the Cantor set has positive Hausdorff dimension.
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Abstract We consider maximal operators in the plane, defined by Cantor sets of directions, and show such operators are not bounded on L2 if the Cantor set has positive Hausdorff dimension.
Key concepts: Mathematics, Cantor set, Cantor function, Cantor's diagonal argument, Bounded function, Hausdorff dimension, Hausdorff measure, Set (abstract data type)