Topological Size of Some Subsets in Certain Calderón–Lozanowskiĭ Spaces

For i = 1,2, 3, let phi(i) be Young functions, (Omega, mu) a (topological) measure space, E an ideal of p-measurable complex valued functions defined on Omega and E-phi i be the corresponding Calderon-Lozanowskii 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) is an element of E-phi 1 x E-phi 2 : vertical bar f vertical bar circle dot vertical bar g vertical bar is an element of E-phi 3} and {(f,g) is an element of E-phi 1 x E-phi 2 : there exists x is an element of V, (f circle dot g)(x) is well defined} where circle dot 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. (C) 2017 Elsevier Inc. All rights reserved.