Superposition operators and functions of bounded $p$-variation

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Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type (2007, methodology): “Definition 4 in Bourdaud, de Cristoforis and Sickel [8], Remark 2 in Sect.”
GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS (2011, background): “eous) Besov space B˙1/2 21 (R), which is suﬃcient, in view of the continuous embedding of B˙1/2 21 (R) into the space V2(R) of functions of quadratic variation (a result due to Peetre—see Theorem 5in [5] for a proof,also the proofof Theorem2 in [33], which applies to p= 2 as well). The seminorm k · ”
Continuous dependence for NLS in fractional order spaces (2010, background): “itions) on gare known so that u→ g(u) is a bounded map of certain Besov spaces. (See e.g. [19] and the references therein.) On the other hand, few works study the continuity of such maps, among which [2, 3, 4, 5, 6]. However, none of these works seems to be easily applicable to such cases as g(u) = ”