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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Morrey space

Author: Cristina T. Zorko
Journal: Proc. Amer. Math. Soc. 98 (1986), 586-592
MSC: Primary 46E35; Secondary 42B30
MathSciNet review: 861756
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Abstract: For $ 1 \leq p < \infty $, $ \Omega $ an open and bounded subset of $ {R^n}$, and a nonincreasing and nonnegative function $ \varphi $ defined in $ (0,{\rho _0}]$, $ {\rho _0} = \operatorname{diam} \Omega $, we introduce the space $ \mathcal{M}_{\varphi ,0}^p(\Omega )$ of locally integrable functions satisfying

$\displaystyle {\inf _{c \in C}}\left\{ {\int\limits_{B({x_0},\rho ) \cap \Omega... ...) - c{\vert^p}dx} } \right\} \leq A\vert B({x_0},\rho )\vert{\varphi ^p}(\rho )$

for every $ {x_0} \in \Omega $ and $ 0 < \rho \leq {\rho _0}$, where $ \vert B({x_0},\rho )\vert$ denotes the volume of the ball centered in $ {x_0}$ and radius $ \rho $. The constant $ A > 0$ does not depend on $ ({x_0},\rho )$.

(i) We list some results on the structure, regularity, and density properties of the space so defined.

(ii) $ \mathcal{M}_{\varphi ,0}^p$ is represented as the dual of an atomic space.

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Keywords: Mean oscillation, Morey space, density, duality
Article copyright: © Copyright 1986 American Mathematical Society

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