In this paper we prove results relating the (parabolic) non-tangential maximum operator and appropriate square functions in Lp for solutions to general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylinders Ω. In particular we prove a global as well as a local and scale i...

We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.

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. 2000 AMS subject classifications: Primary 41A15, 42A45, 42B25, Secondary 42C10, 42B30.

In this paper we prove that the maximal operator of the Marcinkiewicz means of two-dimensional integrable functions with respect to the Walsh–Kaczmarz system is of weak type (1, 1). Moreover, the Marcinkiewicz means Mnf converge to f almost everywhere, for any integrable function f. © 2006 Elsevier Inc. All rights reserved.