A note on Lorentz-Zygmund spaces

作者：Oba Hiroto^*; Sato Enji; Sato Yuichi

来源：Georgian Mathematical Journal, 2011, 18(3): 533-548.

DOI：10.1515/GMJ.2011.0035

• Hausdorff-Young theorem
• Lorentz-Zygmund space

Let 1 <= q < p < infinity, and R be the real line. Hormander showed that any bounded linear translation invariant operator from L-P(R) to L-q(R) is trivial. Blozinski obtained an analogy to Hormander in Lorentz spaces on the real line. In this paper, we generalize Blozinski's result in Lorentz-Zygmund spaces. Also, Bochkarev proved an inequality related to the Hausdorff-Young-Riesz theorem in Lorentz spaces, and the sharpness of the inequality. We improve Bochkarev's inequality in Lorentz-Zygmund spaces, and prove the sharpness of our inequality.

• 出版日期2011