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- W3201450900 abstract "We study the John-Nirenberg space $JN_p$, which is a generalization of the space of bounded mean oscillation. In this paper we construct new $JN_p$ functions, that increase the understanding of this function space. It is already known that $L^p(Q_0) subsetneq JN_p(Q_0) subsetneq L^{p,infty}(Q_0)$. We show that if $|f|^{1/p} in JN_p(Q_0)$, then $|f|^{1/q} in JN_q(Q_0)$, where $q geq p$, but there exists a nonnegative function $f$ such that $f^{1/p} notin JN_p(Q_0)$ even though $f^{1/q} in JN_q(Q_0)$, for every $q in (p,infty)$. We present functions in $JN_p(Q_0) setminus VJN_p(Q_0)$ and in $VJN_p(Q_0) setminus L^p(Q_0)$, proving the nontriviality of the vanishing subspace $VJN_p$, which is a $JN_p$ space version of $VMO$. We prove the embedding $JN_p(mathbb{R}^n) subset L^{p,infty}(mathbb{R}^n)/mathbb{R}$. Finally we show that we can extend the constructed functions into $mathbb{R}^n$, such that we get a function in $JN_p(mathbb{R}^n) setminus VJN_p(mathbb{R}^n)$ and another in $CJN_p(mathbb{R}^n) setminus L^p(mathbb{R}^n)/mathbb{R}$. Here $CJN_p$ is a subspace of $JN_p$ that is inspired by the space $CMO$." @default.
- W3201450900 created "2021-09-27" @default.
- W3201450900 creator A5054796072 @default.
- W3201450900 date "2022-08-16" @default.
- W3201450900 modified "2023-10-18" @default.
- W3201450900 title "Nontrivial examples of $$JN_p$$ and $$VJN_p$$ functions" @default.
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- W3201450900 doi "https://doi.org/10.1007/s00209-022-03100-w" @default.
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