Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials

抄録

Our aim in this paper is to prove the Gagliardo-Nirenberg inequality for Riesz potentials of functions in variable exponent Lebesgue spaces, which are called Musielak-Orlicz spaces with respect to Φ(x,t) = t^p(x)(log(c₀ + t))^q(x) for t > 0 and x ∈ ℝⁿ, via the Littlewood-Paley decomposition.