Akbarbaglu, I.Maghsoudi, S.Seoane-Sepúlveda, Juan B.2023-06-182023-06-18201615787303http://dx.doi.org. 10.1007/s13398-014-0215-1https://hdl.handle.net/20.500.14352/24391In this paper, we consider the size of the set ( f, g) ∈ p(S) × q (S) : ∃ x ∈ S, | f |∗|g|(x) < ∞ , where p ∈ (1, +∞), q ∈ (0, +∞], and S stands for a discrete semigroup. In particular, we prove that if S is an infinite discrete semigroup, p ∈ (1, +∞), q ∈ (1, +∞] with 1/p+1/q < 1, then the set ( f, g) ∈ p(S)×q (S) : | f |∗|g| ∈ ∞(S) is a σ-c-lower porous set in p(S)×q (S)for some c > 0. By means of this notion of porosity we also provide a strengthening of a famous result by Rajagopalan on the p-conjecture.engjournal articlehttp://link.springer.com/article/10.1007/s13398-014-0215-1restricted access517.98Lebesgue spaceσ-c-Lower porous setSemigroupConvolutionAnálisis funcional y teoría de operadores