Capacities and Embeddings of Besov Spaces via General Convolution Kernels

This note is denoted to establish equivalent characterizations of Carleson embeddings of fractional Besov spaces Λ̇^p,q_β (ℝ^n) into the Lorentz spaces L^q_0,p_μ (ℝ^1+n_+) induced by general convolution kernels Φ _t(· ). When (p,q)∈ (1,n/β )× (1,∞ ), the embeddings will be characterized in terms of capacitary type inequalities for open subsets of ℝ^n. When p=q∈ (0,1], the embeddings will be characterized in terms of fractional Besov capacities or the associated variational functional of a nonnegative Radon measure μ . Especially, when p=q=1 and β∈ (0,1), the characterization can be also established in terms of fractional perimeters.