Weighted Weak Type Estimates for Square Functions
Abstract
We consider the weak-type inequality for Littlewood-Paley square functions on Ap weighted Lebesgue spaces. Of interest is the sharp in the Ap 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 Ap characteristic. These estimates improve on known estimates for 1<p<3.
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