One-sided singular integral operators on Calderón-Hardy spaces

S. OMBROSI Y C. SEGOVIA

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

Año: 2003 p. 17 - 35

0041-6932

In [5] we have defined and studied the Hp,+q,(w) spaces for weights w belonging to the class A+s defined by E. Sawyer, and where the parameter is a positive real number. When  is a natural number, these spaces can be identified with the onesided Hardy space Hp+ (w) defined in [7]. In [5] we have defined and studied the Hp,+q,(w) spaces for weights w belonging to the class A+s defined by E. Sawyer, and where the parameter is a positive real number. When  is a natural number, these spaces can be identified with the onesided Hardy space Hp+ (w) defined in [7]. This identification could be used to define a continuous extension of a one-sided regular Calder´on-Zygmund operator from Hp,+q,(w) into Hp,+q,(w), when the parameter is a natural number. In this paper, we give a direct definition of a one-sided regular Calder´on-Zygmund operator on Hp,+q,(w), which is valid for any positive real number , and we prove that these operators can be extended to bounded operators from Hp,+q,(w) into Hp,+q,(w).