Marcinkiewicz multiplier theorem and the Sunouchi operator for Ciesielski-Fourier series

Some classical results due to Marcinkiewicz, Littlewood and Paley are proved for the Ciesielski-Fourier series. The Marcinkiewicz multiplier theorem is obtained for Lp spaces and extended to Hardy spaces. The boundedness of the Sunouchi operator on Lp and Hardy spaces is also investigated.