Geodesic
Characterization of Carleson Measures by the Hausdorff--Young Property
Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 582-590

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It is shown that the Laplace transform of an $L^p$ ($1$) function defined on the positive semiaxis satisfies the Hausdorff–Young type inequality with a positive weight in the right complex half-plane if and only if the weight is a Carleson measure. In addition, Carleson's weighted $L^p$ inequality for the harmonic extension is given with a numeric constant.
Keywords: Hausdorff–Young inequality, Carleson measure, Hardy class, Radon–Nikodym derivative
Mots-clés : Laplace transform, Fourier transform, Poisson integral. 
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     author = {S. Yu. Sadov},
     title = {Characterization of {Carleson} {Measures} by the {Hausdorff--Young} {Property}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {582--590},
     publisher = {mathdoc},
     volume = {94},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a8/}
}
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S. Yu. Sadov. Characterization of Carleson Measures by the Hausdorff--Young Property. Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 582-590. http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a8/