Boundedness of the Hilbert transform on weighted Lorentz spaces
نویسندگان
چکیده
منابع مشابه
On 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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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 obtain estimates for the distribution of values of functions Íll the weighted BMOq, spaces, BMO�(R), that let us find equivalent norms. It is also obtained that a suitable redefinition of the HilbeÍt transform is a bounded operator from these spaces into themselves. This is achieved for a certain cIass of weights w.
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The Hilbert transform is essentially the only singular operator in dimension 1. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on several theoretical and physical problems across a wide range of disciplines; this includes problems in Fourier convergence, complex analysis, potential theory, modulatio...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.05.031