Some weighted norm inequalities for a one-sided version of
Volume 176 / 2006
Studia Mathematica 176 (2006), 21-36
MSC: Primary 42B25, 26A33.
DOI: 10.4064/sm176-1-2
Abstract
We study the boundedness of the one-sided operator g_{\lambda ,\varphi }^+ between the weighted spaces L^p(M^{-}w) and L^p(w) for every weight w. If \lambda = 2/p whenever 1< p< 2, and in the case p=1 for \lambda >2, we prove the weak type of g_{\lambda ,\varphi }^+. For every \lambda >1 and p=2, or \lambda > 2/p and 1< p< 2, the boundedness of this operator is obtained. For p>2 and \lambda >1, we obtain the boundedness of g_{\lambda ,\varphi }^+ from L^p((M^{-})^{[p/2]+1} w) to L^p(w), where (M^{-})^{k} denotes the operator M^{-} iterated k times.
