The bilinear maximal functions map into \(L^p\) for \(2/3 < p \leq 1\). (English) Zbl 0967.47031

Lacey, Michael T.

Ann. Math. (2) 151, No. 1, 35-57 (2000).

The paper contains some results concerning operators of the form: \[ Mfg(x)= \sup_{t>0} \int^t_{-t}|f(x- \alpha y)g(x- y)|dy, \]
\[ T^* fg(x)= \sup_{\varepsilon< \delta}\Biggl|\int_{\varepsilon<|y|< \delta} f(x-\alpha y)g(x- y) K(y) dy\Biggr| \] and so-called “model sums”.

Reviewer: A.Smajdor (Katowice)

MSC:

47G10	Integral operators
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

bilinear maximal functions; bisublinear maximal operators; model sums