Spaceability of sets in Lp x Lq and C0 x C0

A subset E of an infinitely dimensional linearly-topological space X is called spaceable if there is an infinitely dimensional closed subspace Y of X with Y subset of E boolean OR {0}. The main aim of the paper is to show the spaceability of the following sets: 1. the set of those (f,g) E L-p x L-q for which fg is an element of (r) rovided that one of the following conditions holds: (a) 0 < 1/p + 1/q < 1/q and sup{mu(A) : mu(A) < infinity } = infinity (b) 1/p + 1/q > 1/r adn inf {mu(A) : mu(A) > 0 2. the set of those (f, g) E Co x Co for which f g is not integrable, where Co is the space of continuous mappings which vanish at infinity; 3. the set of those (f, g) E LP(G) x Lq(G) for which the convolution f * g is not well-defined or is equal to no provided G is a locally compact but non -compact topological group and p, q > 1 with 1/p -I- 1/q < 1. The paper can be considered as a continuation of our previous ones in which we studied these sets from the Baire category and o" -porosity points of view. (C) 2016 Elsevier Inc. All rights reserved.