JournalspmVol. 81, No. 1/2pp. 127–134

Monotone extremal functions and the weighted Hilbert’s inequality

  • Emanuel Carneiro

    ICTP - The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

  • Friedrich Littmann

    North Dakota State University, Fargo, USA
Monotone extremal functions and the weighted Hilbert’s inequality cover
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Abstract

In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert– Montgomery–Vaughan inequality.

Cite this article

Emanuel Carneiro, Friedrich Littmann, Monotone extremal functions and the weighted Hilbert’s inequality. Port. Math. 81 (2024), no. 1/2, pp. 127–134

DOI 10.4171/PM/2109