Problems on averages and lacunary maximal functions

• Autorzy: Andreas Seeger , James Wright
• Języki publikacji: 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.

Kategorie tematyczne

• 42B15: Multipliers
• 42B25: Maximal functions, Littlewood-Paley theory
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 95
• Numer: 1
• Strony: 235-250

Daty

wydano

2011

Twórcy

autor

Andreas Seeger

• Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA

autor

James Wright

• Maxwell Institute for Mathematical Sciences and the School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland

Identyfikatory

DOI

10.4064/bc95-0-11