On weighted norm inequalities for the Lusin area integral

Segovia, Carlos; Wheeden, Richard L.

doi:10.1090/S0002-9947-1973-0311921-0

On weighted norm inequalities for the Lusin area integral
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by Carlos Segovia and Richard L. Wheeden PDF

Trans. Amer. Math. Soc. 176 (1973), 103-123 Request permission

Abstract:

It is shown that the Lusin area integral for the unit circle is a bounded operator on any weighted ${L^p}$ space, $1 < p < \infty$, on which the conjugate function is a bounded operator. Results are also proved for the case $0 < p \leq 1$.

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