TY - JOUR

T1 - Calderón-Zygmund operators on product Hardy spaces

AU - Han, Yongsheng

AU - Lee, Ming Yi

AU - Lin, Chin Cheng

AU - Lin, Ying Chieh

N1 - Funding Information:
✩ Research by the first author supported in part by NCU Center for Mathematics and Theoretical Physics. Research by the second and third authors supported by both National Science Council and National Center for Theoretical Sciences, Republic of China. * Corresponding author. E-mail addresses: hanyong@auburn.edu (Y. Han), mylee@math.ncu.edu.tw (M.-Y. Lee), clin@math.ncu.edu.tw (C.-C. Lin), linyj@math.ncu.edu.tw (Y.-C. Lin).

PY - 2010/4/15

Y1 - 2010/4/15

N2 - Let T be a product Calderón-Zygmund singular integral introduced by Journé. Using an elegant rectangle atomic decomposition of Hp (Rn × Rm) and Journé's geometric covering lemma, R. Fefferman proved the remarkable Hp (Rn × Rm) - Lp (Rn × Rm) boundedness of T. In this paper we apply vector-valued singular integral, Calderón's identity, Littlewood-Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journé's covering lemma to show that T is bounded on product Hp (Rn × Rm) for max {frac(n, n + ε), frac(m, m + ε)} < p ≤ 1 if and only if T1* (1) = T2* (1) = 0, where ε is the regularity exponent of the kernel of T.

AB - Let T be a product Calderón-Zygmund singular integral introduced by Journé. Using an elegant rectangle atomic decomposition of Hp (Rn × Rm) and Journé's geometric covering lemma, R. Fefferman proved the remarkable Hp (Rn × Rm) - Lp (Rn × Rm) boundedness of T. In this paper we apply vector-valued singular integral, Calderón's identity, Littlewood-Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journé's covering lemma to show that T is bounded on product Hp (Rn × Rm) for max {frac(n, n + ε), frac(m, m + ε)} < p ≤ 1 if and only if T1* (1) = T2* (1) = 0, where ε is the regularity exponent of the kernel of T.

KW - Calderón-Zygmund operators

KW - Journé's class

KW - Littlewood-Paley function

KW - Product Hardy spaces

UR - http://www.scopus.com/inward/record.url?scp=75849127290&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2009.10.022

DO - 10.1016/j.jfa.2009.10.022

M3 - 期刊論文

AN - SCOPUS:75849127290

SN - 0022-1236

VL - 258

SP - 2834

EP - 2861

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -