Hardy-Littlewood-Sobolev Theorem for Bourgain-Morrey Spaces and Approximation
Hardy-Littlewood-Sobolev Theorem for Bourgain-Morrey Spaces and Approximation
In this paper, we establish an extension of the Hardy-Littlewood-Sobolev theorem to the setting of the Bourgain-Morrey space Mαq,p(Rd) (1 ≤ q, p, α ≤ ∞), which theory goes back to Bourgain in 1991. We also prove that Mα q,p(R d ) is included in the closure of the Lebesgue …