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Porosity and the lp-conjecture for semigroups

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Akbarbaglu, I. and Maghsoudi, S. and Seoane-Sepúlveda, Juan B. (2016) Porosity and the lp-conjecture for semigroups. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 110 (1). pp. 7-16. ISSN 15787303

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Official URL: http://link.springer.com/article/10.1007/s13398-014-0215-1



Abstract

In 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.


Item Type:Article
Uncontrolled Keywords:Lebesgue space; σ-c-Lower porous set; Semigroup; Convolution
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:36456
Deposited On:01 Apr 2016 11:56
Last Modified:28 Nov 2016 08:26

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