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arXiv · 1910.11817

Conjugate Transforms on Dyadic Group

Ushangi Goginava·Aleksandre Saatashvili
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Abstract

In this paper we study the properties of the Lebesgue constant of the conjugate transforms. For conjugate Fej\'er means we will find necessary and sufficient condition on $t$ for which the estimation $E\left\vert \widetilde{% \sigma }_{n}^{\left( t\right) }f\right\vert \lesssim E\left\vert f\right\vert $ holds . We also prove that for dyadic irrational $t$, $L\log L $ is maximal Orlicz space for which the estimation $E\left\vert \widetilde{% \sigma }_{n}^{\left( t\right) }f\right\vert \lesssim 1+E\left( \left\vert f\right\vert \log ^{+}\left\vert f\right\vert \right) $ is valid.

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Ushangi Goginava, Aleksandre Saatashvili. 2019-10-25. Conjugate Transforms on Dyadic Group. https://arxiv.org/abs/1910.11817

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