, Volume 26, Issue 2, pp 535-548

Sharp $L^p$ boundedness for a class of square functions

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Abstract

We give the sharp range of boundedness for the square function of Littlewood–Paley type built from dilations of a compactly supported $L^q$ function, filling the gap left for $p<2$ in previous works by several authors. We obtain an improved version if moreover the function from which the square operator is built is assumed to be radial.

Supported in part by the Grants MTM2007-62186 of MEC (Spain) and FEDER, and IT-305-07 of the Basque Government.