Abstract
The spaces A sp,q (ℝn)with A ∈ {B, F}, s ∈ ℝ and 0 <p,q ≤ ∞ are usually introduced in terms of Fourier-analytical decompositions. Related characterizations based on atoms and wavelets are known nowadays in a rather final way. Quarks atomize the atoms into constructive building blocks. It is the main aim of this survey to raise quarkonial decompositions to the same level as related representations of the spaces A sp,q (ℝn) in terms of atoms or wavelets culminating finally in universal frame representations of tempered distributions f ∈ S′(ℝn).
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Dedicated to Professor Oleg V. Besov on the occasion of his 90th birthday
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Triebel, H. Building Blocks in Function Spaces. Anal Math 49, 1107–1136 (2023). https://doi.org/10.1007/s10476-023-0236-0
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DOI: https://doi.org/10.1007/s10476-023-0236-0