Multidimensional rearrangement and Lorentz spaces
نویسندگان
چکیده
We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces. Mathematics Subject Classification 2000: 46E30, 46B25.
منابع مشابه
Mixed norm and multidimensional Lorentz spaces
Abstract. In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing r...
متن کاملSharp constants related to the triangle inequality in Lorentz spaces
The study of the normability of the Lorentz spaces L(R, μ) goes back to the work of G.G. Lorentz [10, 11] (see also [13, 3, 2] for a more recent account of the normability results for the weighted Lorentz spaces). The condition defining these spaces is given in terms of the distribution function and, equivalently, the non-increasing rearrangement of f (see [1] for standard notations and basic d...
متن کاملComparison of Orlicz–Lorentz Spaces
Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Masty lo, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz–Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a...
متن کاملar X iv : 1 40 1 . 59 06 v 5 [ m at h . FA ] 3 S ep 2 01 4 NONLINEAR SUBSETS OF FUNCTION SPACES AND SPACEABILITY
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...
متن کاملOn the Bouundedness of Fractional B-maximal Operators in the Lorentz Spaces
In this study, sharp rearrangement inequalities for the fractional Bmaximal function Mα,γf are obtained in the Lorentz spaces Lp,q,γ and by using these inequalities the boundedness conditions of the operator Mα,γ are found. Then, the conditions for the boundedness of the Bmaximal operator Mγ are obtained in Lp,q,γ .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008