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Weighted Weak Type Estimates for Square Functions

Research paper by Michael T Lacey, James Scurry

Indexed on: 18 Nov '12Published on: 18 Nov '12Published in: Mathematics - Classical Analysis and ODEs



Abstract

We consider the weak-type inequality for Littlewood-Paley square functions on A_p weighted Lebesgue spaces. Of interest is the sharp in the A_p characteristic estimate. The case of 1<p<2 is subcritical, and the sharp power of 1/p is established. In the critical case of p=2, we miss the critical exponent 1/2 by a logarithm of the A_p characteristic. These estimates improve on known estimates for 1<p<3.