Restricting Riesz–Logarithmic-Gagliardo–Lipschitz Potentials

Abstract

For s ∈ [0, 1], b ∈ ℝ and p ∈ [1, ∞), let \(\dot{B}_{p,\infty}^{s,b}(\mathbb{R}^{n})\) be the logarithmic-Gagliardo–Lipschitz space, which arises as a limiting interpolation space and coincides to the classical Besov space when b = 0 and s ∈ (0, 1). In this paper, the authors study restricting principles of the Riesz potential space \(\cal{I}_{\alpha}(\dot{B}_{p,\infty}^{s,b}(\mathbb{R}^{n}))\) into certain Radon–Campanato space.