Besov and Triebel-Lizorkin Spaces Related to Singular Integrals with Flag Kernels

Abstract

Let s₁, s₂ Є (—1, 1) and s = (s₁, s₂). In this paper, the author introduces the Besov space B^s_pqq(R²) with p, q Є [1, ∞] and the Triebel-Lizorkin space F^s_pqq(R²) with p Є (1, ∞) and q Є (1, ∞] associated to singular integrals with flag kernels. Some basic properties, including their dual spaces, some equivalent norm characterizations via Littlewood-Paley functions, lifting properties and some embedding theorems, on these spaces are given. Moreover, the au thor obtains the boundedness of flag singular integrals and fractional integrals on these spaces.