DYADIC DERIVATIVES AND A WEAK TYPE INEQUALITY FOR MAXIMAL FUNCTIONS
Abstract
We prove that if a continuous function f on (0,1) has a dyadic derivative for every x (ELEM) (0,1), then f is constant on (0,1). This generalizes a theorem of Butzer and Wagner. We also give a condition which is equivalent to a weak type inequality for certain maximal functions.
Degree
Ph.D.
Subject Area
Mathematics
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