Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups equipped with Haar measure

Abstract

We prove that the Grand Lebesgue Space built on a unimodular locally compact topological group, equipped with bi‐invariant Haar measure, forms a Banach algebra relative to the convolution.

Bochner–Riesz operators in grand lebesgue spaces

“…[10,23,25,28,30,36,37,4,5]). For example they play an important role in the theory of Partial Differential Equations (PDEs) (see, e.g., [2,12,14,22,21]), in interpolation theory (see, e.g., [1,13,15,16]), in Functional Analysis (see, e.g., [11,17,18]), in the theory of Probability ( [9,23,27,29,30,19,20]), in Statistics ( [23,30,32], [27, chapter 5]), in theory of random fields ( [23,27,34]).…”

Bochner-Riesz operators in Grand Lebesgue spaces

“…Recently in [20] has been given a generalization of the convolution inequality in the context of the Grand Lebesgue Spaces (see Section 3 for the definition), built on a unimodular locally compact topological group.…”