Littlewood-Paley operators on BMO

Kurtz, Douglas S.

doi:10.1090/S0002-9939-1987-0877035-1

Littlewood-Paley operators on BMO
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Proc. Amer. Math. Soc. 99 (1987), 657-666 Request permission

Abstract:

Two Littlewood-Paley operators, the area integral and the function $g_\lambda ^ *$, are considered as operators on functions of bounded mean oscillation. It is proved that the image of a BMO function under one of these operators is either equal to infinity almost everywhere or is in BMO.

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