Lorentz-Shimogaki and Boyd theorems for weighted Lorentz spaces
نویسندگان
چکیده
We prove the Lorentz-Shimogaki and Boyd theorems for the spaces Λu(w). As a consequence, we give the complete characterization of the strong boundedness of H on these spaces in terms of some geometric conditions on the weights u and w, whenever p > 1. For these values of p, we also give the complete solution of the weak-type boundedness of the Hardy-Littlewood operator on Λu(w).
منابع مشابه
A New Characterization of the Muckenhoupt Ap Weights Through an Extension of the Lorentz-Shimogaki Theorem
Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index ᾱX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator mλf . It is shown then that the Hardy-Littlewood maximal operator M is bounded on X if and only if αX < 1 providing an extension of the classical theorem of Lorentz and ...
متن کاملD ec 1 99 9 Boyd Indices of Orlicz – Lorentz Spaces STEPHEN
Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska–Orlicz indices of the defining functions are given. Also, we give an example to show that the Boyd indices and Zippin indices of an Orlicz–Lorentz space need not be equal, answering a question of Malig...
متن کاملBoyd Indices of Orlicz–Lorentz Spaces
Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska–Orlicz indices of the defining functions are given. Also, we give an example to show that the Boyd indices and Zippin indices of an Orlicz–Lorentz space need not be equal, answering a question of Malig...
متن کاملFrom the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups
The Lorentz transformation of order $(m=1,n)$, $ninNb$, is the well-known Lorentz transformation of special relativity theory. It is a transformation of time-space coordinates of the pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and $n$ space dimensions ($n=3$ in physical applications). A Lorentz transformation without rotations is called a {it boost}. Commonly, the ...
متن کاملMixed 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. London Math. Society
دوره 89 شماره
صفحات -
تاریخ انتشار 2014