Topological size of some subsets in certain Calderón-LozanowskiÄ­ spaces

For i=1,2,3, let φi be Young functions, (Ω,μ) a (topological) measure space, E an ideal of μ-measurable complex-valued functions defined on Ω and Eφi be the corresponding Calderón-LozanowskiÄ­ space. Our aim in this paper is to give, under mild conditions, several results on topological size (in the sense of Baire) of the sets {(f,g)∈Eφ1×Eφ2:|f|⨀|g|∈Eφ3} and {(f,g)∈Eφ1×Eφ2:∃x∈V,(f⨀g)(x) is well defined} where ⨀ denotes the convolution or pointwise product of functions and V a compact neighborhood. Our results sharpen and unify the related results obtained in diverse areas during recent thirty years.