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Eurasian Mathematical Journal, 2013, Volume 4, Number 1, Pages 54–64
(Mi emj114)
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This article is cited in 2 scientific papers (total in 2 papers)
New characterization of Morrey spaces
A. Gogatishvilia, R. Ch. Mustafayevbc a Institute of Mathematics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic
b Department of Mathematics, Faculty of Science and Arts, Kirikkale University, Yahsihan, Kirikkale, Turkey
c Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan
Abstract:
In this paper we prove that the norm of the Morrey space $\mathcal{M}_{p,\lambda}$ is equivalent to
$$
\sup\left\{\int_{\mathbb{R}^n}|fg|: \inf_{x\in\mathbb{R}^n}\int_0^\infty r^{\frac{n-\lambda}p-1}||g||_{L_{p'}(^\complement B(x,r))}dr\leqslant1\right\}.
$$
Keywords and phrases:
local Morrey-type spaces, complementary local Morrey-type spaces, associate spaces, dual spaces.
Received: 03.10.2011
Citation:
A. Gogatishvili, R. Ch. Mustafayev, “New characterization of Morrey spaces”, Eurasian Math. J., 4:1 (2013), 54–64
Linking options:
https://www.mathnet.ru/eng/emj114 https://www.mathnet.ru/eng/emj/v4/i1/p54
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