Some Properties Of Anisotropic Weak Hardy Spaces Of Musielak-Orlicz Type And Their Application

The real-variable theory of Hardy spaces plays an important role in harmonic analy-sis, which has important applications in various fields of analysis and partial differential equations. Let cp be an anisotropic Musielak-Orlicz function with growth assumptions and A an expansive dilation. We mainly studies some properties of anisotropic weak Hardy spaces of Musielak-Orlicz type and their application.Precisely, this article is organized as follows.In Chapter 1, we introduce the background, current research situation and the main results of and related operators.In Chapter 2, we first recall the definitions of the anisotropic growth function and introduce the anisotropic weak Hardy space of Musielak-Orlicz type. Then we obtain some real-variable characterizations of in terms of the radial, the non-tangential and the tangential maximal functions via a new monotone convergence theo-rem adapted to the weak anisotropic Musielak-Orlicz space. As an application, we show the boundedness of a class of multilinear operators formed by the anisotropic Calderon-Zygmund operators from product weighted Lebesgue space to with ?(x, t):=tp?(x),p?(0,1]and ??A1(A).In Chapter 3, By using the atomic decomposition of we obtain the bound-edness of the anisotropic Littlewood-Paley Lusin-area function, the anisotropic g-function and the anisotropic function from to weak Musielak-Orlicz-type space...