2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability

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Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, background): “Subsequently, Vyb́ıral [72] established Sobolev and Jawerth embeddings of these spaces and, moreover, Kempka [34] characterized F s(·) p(·),q(·)(R n) by local means, and Kempka and Vyb́ıral [36] obtained the equivalent characterization via ball means of differences.”
Besov-Type Spaces with Variable Smoothness and Integrability (2015, methodology): “More generally, 2-microlocal Besov and Triebel-Lizorkin spaces with variable, B w(·) p(·),q(·)(R ) and F w(·) p(·),q(·)(R ), were introduced by Kempka [27, 28] and provided a unified approach that cover the classical Besov and Triebel-Lizorkin spaces as well as versions of variable smoothness and in”
Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, methodology): “Juni 136, 10623 Berlin, Germany e-mail: vybiral@math.tu-berlin.de”
Besov spaces with variable smoothness and integrability (2010, background): “These studies were all restricted to bounded exponents p and q. Vyb́ıral [43] and Kempka [23] also considered Besov spaces B α(·) p(·),q—note that only the case of constant q was included.”
Atomic, molecular and wavelet decomposition of 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability (2010, methodology): “8 which is proved in [22].”