We characterize boundedness of a convolution operator with a fixed kernel between the classes , defined in terms of oscillation, and weighted Lorentz spaces , defined in terms of the maximal function, for . We prove corresponding weighted Young-type inequalities of the form
and characterize the optimal rearrangement-invariant space for which these inequalities hold.
Cite this article
Martin Křepela, Convolution in Rearrangement-Invariant Spaces Defined in Terms of Oscillation and the Maximal Function. Z. Anal. Anwend. 33 (2014), no. 4, pp. 369–383DOI 10.4171/ZAA/1517