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The bridge regression is a least squares problem with penalty function $\lambda \sum_{j=1}^p|\beta_j|^q$ that nests e.g. the well known LASSO regression. Several sources state that the regression gives "sparse" solutions when $q\leq 1$, e.g. https://www.intlpress.com/site/pub/files/_fulltext/journals/sii/2013/0006/0002/SII-2013-0006-0002-a007.pdf (where it is stated only as a known fact). What would be a good source for a proof of this statement?

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