Boundedness of one-sided fractional integrals in the one-sided Calderon-Hardy spaces

In this paper we study the mapping properties of the one-sided fractional integrals in the Calderon-Hardy spaces H-q,alpha(p,+ )(omega) for 0 < p <= 1, 0 < alpha < infinity and 1 < q < infinity. Specifically, we show that, for suitable values of p,q,gamma,alpha and s, if omega is an element of A(s)(+) (Sawyer's classes of weights) then the one-sided fractional integral I-gamma(+) can be extended to a bounded operator from H-q,alpha(p,+) (omega to H-q,alpha+gamma(p,+ )(omega). The result is a consequence of the pointwise inequality N-q,alpha+gamma(+) (I-gamma(+) F;x) <= C alpha,gamma Nq,alpha+ (F;X), where N-q,alpha(+)(F;x) denotes the Calderon maximal function.