MASTYLO , Mieczyslaw

We investigate variants of the maximal operator and show their applications to study boundedness of the classical Hardy-Littlewood maximal operator between weighted Banach function spaces which satisfy certain geometrical lattice conditions. We prove inequalities for rearrangement of the maximal operators generated by rearrangement invariant...

Consider two continuous linear operators T : X1(μ) ! Y1( ) and S : X2(μ) ! Y2( ) between Banach function spaces related to different -finite measures μ and . We characterize by means of weighted norm inequalities when T can be strongly factored through S, that is, when there exist functions g and h such that T (f) = gS(hf) for all f 2...

We study the connections between the Kadec-Klee property for local convergence in measure H`, the Kadec-Klee property for global onvergence in measure Hg and the ∆2-condition for Orlicz function spaces Lϕ equipped with either the Luxemburg norm k · kϕ or the Orlicz norm k · k0 ϕ. Nominally, we prove that for (Lϕ, k · kϕ) the conditions: ϕ...