BOUNDEDNESS OF CALDERON-ZYGMUND OPERATORS ON WEIGHTED PRODUCT HARDY SPACES

作者：Lee Ming Yi^*

来源：Journal of Operator Theory, 2014, 72(1): 115-133.

DOI：10.7900/jot.2012nov06.1993

• Calderon-Zygmund operator
• Littlewood-Paley theory
• weighted product Hardy space

Let T be a singular integral operator in Journe%26apos;s class with regularity exponent epsilon, omega is an element of A(q), 1 %26lt;= q %26lt; 1 + epsilon, and q/(1 - epsilon) %26lt; p %26lt;= 1. We obtain the H-omega(p)(R x R)-L-omega(p) (R-2) boundedness of Thy using R. Fefferman%26apos;s %26quot;trivial lemma%26quot; and Journe%26apos;s covering lemma. Also, using the vector-valued version of the %26quot;trivial lemma%26quot; and Littlewood-Paley theory, we prove the H-omega(p)(R x R)-boundedness of T provided T-1*(1) = T-2*(1) = 0; that is, the reduced T1 theorem on H-omega(p)(R x R). In order to show these two results, we demonstrate a new atomic decomposition of H-omega(p)(R x R) boolean AND L-omega(2) (R-2), for which the series converges in L-omega(2). Moreover, a fundamental principle that the boundedness of operators on the weighted product Hardy space can be obtained simply by the actions of such operators on all atoms is given.

• 出版日期2014
• 单位中央民族大学