Full paper in PDF format:
$%D. Yang, Besov and Triebel-Lizorkin spaces related to singular integrals with flag kernels, Rev. Mat. Complut. 22 (2009), no. 1, 253–302.%$

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

Dachun YANG

School of Mathematical Sciences
Beijing Normal University
Laboratory of Mathematics and Complex Systems
Ministry of Education
Beijing 100875 — People’s Republic of China
dcyang@bnu.edu.cn

Received: August 11, 2008
Accepted: January 8, 2009

ABSTRACT

Let $s1,s2 ∈(- 1,1)$ and $s= (s1,s2)$ . In this paper, the author introduces the Besov space $˙s 2 Bpq(ℝ )$ with $p,q ∈[1,∞ ]$ and the Triebel-Lizorkin space $˙s 2 Fpq(ℝ )$ with $p ∈ (1,∞ )$ and $q ∈ (1,∞ ]$ 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 author obtains the boundedness of flag singular integrals and fractional integrals on these spaces.

Key words: Besov space, Triebel-Lizorkin space, flag singular integral, flag fractional integral, Littlewood-Paley operator, dual space, lifting, embedding.
2000 Mathematics Subject Classification: 42B35, 42B20, 42B25, 46E35.