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A note on quarkonial systems and multilevel partition of unity methods


  • Dedicated to Professor Hans Triebel


We discuss the connection between the theory of quarkonial decompositions for function spaces developed by Hans Triebel, and the multilevel partition of unity method. The central result is an alternative approach to the stability of quarkonial decompositions in Besov spaces equation image, s > n(1/p − 1)+, which leads to relaxed decay assumptions on the elements of a quarkonial system as the monomial degree grows.