Juhl's formulae for GJMS operators and Q-curvatures

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Direct proofs are given of Juhl's formulae for GJMS operators and Q-curvatures starting from the original construction of GJMS.

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The Nirenberg problem and its generalizations: a unified approach (2014, methodology): “Recently, an explicit formula and a recursive formula for GJMS operators and Q-curvatures have been found by Juhl [55,56] (see also Fefferman and Graham [35]).”
On Fractional GJMS Operators (2014, background): “ φ | 2 + 1 m Ym φ 2 + m+n+1 2 Jm φ 2 the weighted Q-curvature; our sign convention is ∆φ = δφdon functions. Recursive formulae for the GJMS operators of all orders were found by Juhl [28]; see also [13]. In principle, these formulae can be extended to the weighted GJMS operators, though at present ”