Multipliers of grand and small Lebesgue spaces

Abstract

Let $G$ a locally compact abelian group with Haar measure $\mu$ and let $1<p<\infty .$ In the present paper we determine necessary and sufficient conditions on $G$ for the grand Lebesgue space $L^{p),\theta }(G)$ to be a Banach algebra under convolution.Later we characterize the multipliers of the grand Lebesgues, $L^{p,)\theta }(G)$ and the small Lebesgue spaces $L^{(P^{\prime }\theta }$, where $\frac{1}{p}+\frac{1}{p^{\prime }}=1$

7 pages. arXiv admin note: text overlap with arXiv:1901.07282

Cited by in corpus (2)

• Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups
• Restricted version of Grand Lebesgue Spaces