منابع مشابه
The Fourier Transform in Weighted Lorentz Spaces
Abstract Necessary conditions and sufficient conditions on weights u and w are given for the Fourier transform F to be bounded as a map between the Lorentz spaces Γq(w) and Λp(u). This may be viewed as a weighted extension of a result of Jodeit and Torchinsky on operators of type (1,∞) and (2, 2). In the case 0 < p ≤ 2 = q, the necessary and sufficient conditions are equivalent and give a simpl...
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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).
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We establish necessary and sufficient conditions for imbeddings of weighted Orlicz–Lorentz spaces.
متن کاملFourier Multipliers on Weighted L-spaces
In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type (p, p) on Lp(Rn) if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery’s result is sharp in a certain sense. We also obtain a weighted analogue of Carbery’s result. Some applications of our results are also given.
متن کاملOn the Boundedness of Classical Operators on Weighted Lorentz Spaces
Conditions on weights u(·), v(·) are given so that a classical operator T sends the weighted Lorentz space Lrs(vdx) into Lpq(udx). Here T is either a fractional maximal operator Mα or a fractional integral operator Iα or a Calderón–Zygmund operator. A characterization of this boundedness is obtained for Mα and Iα when the weights have some usual properties and max(r, s) ≤ min(p, q). § 0. Introd...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2015
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-015-9455-5