×

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

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”.

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.)
PDFBibTeX XMLCite
Full Text: DOI arXiv EuDML Link