Problems on Averages and Lacunary Maximal Functions
نویسنده
چکیده
We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H to L bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an Lp regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an L regularity result for such averages. We formulate various open problems.
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