A NOTE ON CONVOLUTION-TYPE CALDERóN-ZYGMUND OPERATORS

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

【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 Hrmander condition can ensure the boundedness on Triebel-Lizorkin spaces ■ p 0 ,q(1 < p, q < ∞) and on a party of endpoint spaces ■1 0 ,q(1 ≤ q ≤ 2), but this idea is invalid for endpoint Triebel-Lizorkin spaces ■1 0 ,q(2 < q ≤ ∞). In this article, the authors apply wavelets and interpolation theory to establish the boundedness on ■1 0 ,q(2 < q ≤ ∞) under an integrable condition which approaches Hrmander condition infinitely.更多还原