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.

The final objective of our study is to propose a finite dimensional approach to systems of parabolic partial differential equations perturbed by low order noises of Brownian or fractional Brownian type. The present paper is the preparatory first part, where we introduce partial pathwise integrals over D and (a, b) × D, where D is a smooth bounded domain in R. Corresponding stochastic versions a...

In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0, 1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular. We consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative for Marci...

In this paper we propose a method of regularizing the backwards parabolic partial differential equations that arise from using gradient descent to minimize surface energy integrals within a level set framework in 2 and 3 dimensions. The proposed regularization energy is a functional of the mean curvature of the surface. Our method uses a local level set technique to evolve the resulting fourth ...

Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz spa...

We study quadratic integrability of systems with velocity dependent potentials in three-dimensional Euclidean space. Unlike the case only scalar potential, does not imply separability configuration The leading order terms pairs commuting integrals can either generalize or have no relation to forms separation absence a vector potential. call such generalized, distinguish them from standard ones,...

Baum and Katz (Trans. Am. Math. Soc. 120:108-123, 1965) obtained convergence rates in the Marcinkiewicz-Zygmund law of large numbers. Their result has already been extended to the short-range dependent linear processes by many authors. In this paper, we extend the result of Baum and Katz to the long-range dependent linear processes. As a corollary, we obtain convergence rates in the Marcinkiewi...

This article is concerned with the question of whether Marcinkiewicz multipliers on R2n give rise to bilinear multipliers on R×R. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers f...