Acta mathematica scientia, Series B >
A NOTE ON CONVOLUTION-TYPE CALDERÓN-ZYGMUND OPERATORS
Received date: 2007-03-28
Revised date: 2008-09-30
Online published: 2009-09-20
Supported by
Sponsored by the NSF of South-Central University for Nationalities (YZZ08004) and the Doctoral programme
foundation of National Education Ministry of China
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 Fp0,q(1< p, q < ∞) and on a party of endpoint spaces F10,q(1 ≤ q ≤ 2), but this idea is invalid for endpoint Triebel-Lizorkin spaces F10,q(2 < q ∞). In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F10,q(2 < q ≤ ∞) under an integrable condition which
approaches Hörmander condition infinitely.
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 . DOI: 10.1016/S0252-9602(09)60107-7
[1] Deng D G, Yan L X, Yang Q X. On Hörmander condition. Chinese Science Bulletin, 1997, 42(10): 1341--1345
[2] Yang Q X. The smallest regularity index for T1 theorem on Hardy space. Preprint
[3] Yang Z Y, Yang Q X. Convolution-type Calderón-Zygmund operators and approximation (In Chinese). Acta Math Sinica, 2008, 56(6): 1061--1072
[4] Yabuta K. Generalization of Calder\'{o}n-Zygmund operators. Studia Math, 1985, 82(1): 17--31
[5] Triebel H. Theory of Function Spaces. Basel: Birkhäuser Verlag, 1983
[6] Yang Q X. Wavelets and Distribution (In Chinese). Beijing: Beijing Science and Technology Press, 2002
[7] Meyer Y, Yang Q X. H\"{o}rmander conditions and T1 theorems in general context//Liu P D, ed. Functional Space Theory and Its Applications (Proceedings of International Conference & 13th Academic Symposium in China). Research Information Ltd UK, 2003: 169--172
[8] Frazier M, Jawerth B, Han Y S, Weiss G. The T1 theorem for Triebel-Lizorkin spaces//Proceeding of the Conference on Harmontic Analysis and PDE, EI Escorial 1987. Lectures Notes in Math 1384. Berlin: Springer-Verlag, 1989
[9] Yang Q X. Characterization of singular integral kernel space and T(1) theorem. Tokyo J Math, 2000, 23(2): 361--372
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