关键词: convolution type Calderón Zygmund operators, Triebel Lizorkin spaces, wavelets, atomic decomposition

Abstract:

For convolution-type Calderón-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is  known that Hörmander condition can ensure the boundedness on
Triebel-Lizorkin spaces F_p^0,q(1< p, q < ∞)  and on a party of endpoint spaces F₁^0,q(1 ≤ q ≤ 2), but this idea is invalid for endpoint Triebel-Lizorkin spaces F₁^0,q(2 < q ∞). In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F₁^0,q(2 < q ≤ ∞) under an integrable condition which
approaches Hörmander condition infinitely.

Key words: convolution type Calderón Zygmund operators, Triebel Lizorkin spaces, wavelets, atomic decomposition