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• # Artykuł - szczegóły

## Banach Center Publications

2011 | 95 | 1 | 235-250

## Problems on averages and lacunary maximal functions

EN

### Abstrakty

EN
We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H¹ to $L^{1,∞}$ bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an $L^p$ regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L² boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an $L^p$ regularity result for such averages. We formulate various open problems.

235-250

wydano
2011

### Twórcy

autor
• Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA
autor
• Maxwell Institute for Mathematical Sciences and the School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland