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2021 Functional Calculus on BMO-type Spaces of Bourgain, Brezis and Mironescu
Liguang LIU, Dachun YANG, Wen YUAN
Tokyo J. Math. Advance Publication 1-27 (2021). DOI: 10.3836/tjm/1502179329

Abstract

A nonlinear superposition operator $T_g$ related to a Borel measurable function $g:\ {\mathbb C}\to {\mathbb C}$ is defined via $T_g(f):=g\circ f$ for any complex-valued function $f$ on ${\mathbb R^n}$. This article is devoted to investigating the mapping properties of $T_g$ on a new BMO type space recently introduced by Bourgain, Brezis and Mironescu [J. Eur. Math. Soc. (JEMS) 17 (2015), 2083--2101], as well as its VMO and CMO type subspaces. Some sufficient and necessary conditions for the inclusion and the continuity properties of $T_g$ on these spaces are obtained.

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Liguang LIU. Dachun YANG. Wen YUAN. "Functional Calculus on BMO-type Spaces of Bourgain, Brezis and Mironescu." Tokyo J. Math. Advance Publication 1 - 27, 2021. https://doi.org/10.3836/tjm/1502179329

Information

Published: 2021
First available in Project Euclid: 11 December 2020

Digital Object Identifier: 10.3836/tjm/1502179329

Subjects:
Primary: 46E35
Secondary: 42B35, 46E30

Rights: Copyright © 2021 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
27 PAGES

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