Abstract:To shed some light on the John-Nirenberg space, the authors in this article introduce the John-Nirenberg-Q space via congruent cubes, JNQ α p,q (R n ), which when p = ∞ and q = 2 coincides with the space Q α (R n ) introduced by Essén et al. in [Indiana Univ. Math. J. 49 (2000), 575-615]. Moreover, the authors show that, for some particular indices, JNQ α p,q (R n ) coincides with the congruent John-Nirenberg space, or that the (fractional) Sobolev space is continuously embedded into JNQ α p,q (R n ). Further… Show more
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