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A short proof of an inequality of Littlewood and Paley

Authors:	Miroslav Pavlovic

Institution:	Matematicki Fakultet, Univerzitet u Beogradu, Studentski trg 16, 11000 Belgrade, Serbia, Yugoslavia

Abstract:	A very short proof is given of the inequality $\displaystyle \int_{\vert z\vert<1}\vert\nabla u(z)\vert^p (1-\vert z\vert)^{p-... ...rac 1{2\pi}\int_0^{2\pi} \vert f(e^{it})\vert^p\,dt -\vert u(0)\vert^p\right),$ where and is the Poisson integral of $f\in L^p(\partial \mathbb{D}),$ $\mathbb{D}=\{z: \vert z\vert<1\}.$

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