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Given a positive multilinear operator M P X1) × P X2) × … ×P Xn) → P Xn+1), and fixed indices p1, p2,…, pn, qϵ [1, ∞], we consider the problem of determining those nonnegative (weight) functions w1, w2,…, wn and v on X1, X2,…, Xn and Xn + 1, respectively, for which Xn+112nqn+11q ⩽C Xjjjpj1pj, with C > 0 independent of fjϵP Xj), j=1,2, …, n.
Let T be an m-linear operator, and let 1 < q 1, …, q m < ∞ and 1 m < q < ∞ be fixed indices such that 1 q = 1 q 1 + ⋯ + 1 q m.
Using the quasi-norm of B p, τ α ( A ), the main result is formulated in Theorem 5 as two inequalities, estimating the minimal distance from a given element to a subspace of exponential type vectors with fixed indices.
In stationary phantom test objects with fixed indices, our process did recover the expected reference values with little variability in repeated measures for central thickness.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com