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In this paper we study warped products endowed with a new semi-symmetric non-metric connection, which, we called Diallo-Massamba connection. We establish relationships between the Diallo-Massamba connection of the warped product to those of the base and the fiber. Also, we derive the curvature formulas for warped products with the Diallo-Massamba connection in terms of curvatures of its components. Examples of Diallo-Massamba connection are also given.
The aim of this paper is to give an overview of some inequalities about Lp-norms (p = 1 or p = 2) of harmonic (periodic) and non-harmonic trigonometric polynomials. Among the material covered, we mention Ingham’s Inequality about L2 norms of non-harmonic trigonometric polynmials, the proof of the Littlewood conjecture by McGehee, Pigno and Smith on the lower bound of the L1 norm of harmonic trigonometric polynomials as well as its counterpart in the non-harmonic case due to Nazarov. For the later one, we give a quantitative estimate that completes our recent result with an estimate of L1-norms over small intervals. We also give some stronger lower bounds when the frequencies satisfy some more restrictive conditions (lacunary Fourier series, “multi-step arithmetic sequences”). Most proofs are close to existing ones and some open questions are mentionned at the end.
In this note we revise the perturbation result of [7] on the prescribed Branson-Paneitz curvature problem on the n-dimensional unit sphere, n ≥ 6. We remove condition (A1) of ([7], Theorem 1.3) and we prove an entirely new perturbation theorem.
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