A NOTE ON CONVOLUTION-TYPE CALDERÓN-ZYGMUND OPERATORS

doi:10.1016/S0252-9602(09)60107-7

Abstract

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

CLC Number:

42B20

Cite this article

YANG Zhan-YIng, YANG Qi-Xiang. A NOTE ON CONVOLUTION-TYPE CALDERÓN-ZYGMUND OPERATORS[J].Acta mathematica scientia,Series B, 2009, 29(5): 1341-1350.

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