ABSTRACT. In [5J we have defined and studied the 1t�:;t(w) spaces for weights w belonging to the class A;; definecl by E. Sawyer, ancl where the parameter a is a positive real number. When a is a natural number, these spaces can be identifiecl with the one-sidecl Hardy space H � (w) clefinecl in [7J. This identifieation could be used to define a eontinuous extension of a one-sided regular Calderón-Zygmund operator from 1í�:;t(w) into 1t�:;t(w), when the parameter a is a natural number. In this paper, we give a direct definition of a one-sided regular Calderón-Zygmund operator on Aa n1í�:;(w), which is valid for any real number a> 0, and we prove that these operators can be extended to bouncled operators from 1í�:;t (w) into 1t�:;t (w)
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