The purpose of this paper is to prove a necessary and sufficient condition for a vanishing mean oscillation function. To obtain this result we use an extension to Morrey spaces of an inequality by Fefferman and Stein concerning the maximal and the sharp maximalfunction, the fractional maximal function used by Muckenhoupt and Wheeden and the spaces generated by blocks well studied by Shirai, Komori and Mizuhara.

Necessary and sufficient condition for a VMO function

RAGUSA, Maria Alessandra
2012-01-01

Abstract

The purpose of this paper is to prove a necessary and sufficient condition for a vanishing mean oscillation function. To obtain this result we use an extension to Morrey spaces of an inequality by Fefferman and Stein concerning the maximal and the sharp maximalfunction, the fractional maximal function used by Muckenhoupt and Wheeden and the spaces generated by blocks well studied by Shirai, Komori and Mizuhara.
Vanishing mean oscillation; Singular integral operators; Morrey spaces
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/8817
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