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arXiv · 2610.41309

Product Pitt inequalities and signed Boas equivalences for general monotone functions

Niyaz Tokmagambetov
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Abstract

We prove product-weight Pitt inequalities for real or complex functions on $\mathbb R^d$ whose full mixed Vitali variation satisfies an exterior-tail general monotonicity condition. A two-parameter condition gives spatial weights with different powers near the coordinate hyperplanes and at infinity. For the classical parameters, a reverse estimate yields a Boas norm equivalence without sign, parity or separability assumptions. The equivalence holds for finite spatial norm and, for $L^1$ data, characterizes finiteness of either norm; the unrestricted nonintegrable converse remains open. We also prove an equivalence under primitive control, give explicit examples, and establish sharpness of the Fourier-side exponent range.

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Niyaz Tokmagambetov. 2026-10-30. Product Pitt inequalities and signed Boas equivalences for general monotone functions. https://arxiv.org/abs/2610.41309

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