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The central BMO spaces and Littlewood-Paley operators. (English) Zbl 0857.42009

Let 1<p<. A function fL loc p ( n ) is said to belong to CBMO p ( n ) (central bounded mean oscillation space), if

sup r>0 |B(r)| -1 B(r) |f(x)-f B(r) | p d x 1/p <,

where f B(r) is the integral mean of f over the ball B(r) with center at the origin and radius r. This space is a local version of the usual BMO( n ), and a dual space of a kind of Hardy space associated with the Herz space. The authors give a characterization of CBMO 2 ( n ) in terms of the central Carleson measure. Using this, they give some results on CBMO 2 ( n ) boundedness of several classes of general Littlewood-Paley operators.

Reviewer: K.Yabuta (Nara)
42B25Maximal functions, Littlewood-Paley theory
42B30H p -spaces (Fourier analysis)