Inclusions and Noninclusions of Spaces of Multipliers of Some Wiener Amalgam Spaces

Abstract

The main purpose of this paper is to study inclusions and noninclusions among the spaces of multipliers of the Wiener amalgam spaces. M. G. Cowling and J. J. F. Fournier in [5], L. Hormander in [22] and G. I. Gaudry in [15], have worked on the space M-G(L-p, L-q), the space of convolution multipliers from L-p into L-q, and studied inclusions and noninclusions among these spaces. In this paper, we consider much larger classes of spaces than L-p and L-q : we consider the Wiener amalgam spaces W(L-p, L-q) and weighted Wiener amalgam spaces W(L-p, L-omega(q)). Firstly, we work on inclusions between the spaces of multipliers of Wiener amalgam spaces. Later by using the Rudin-Shapiro measures, we investigate noninclusions among the spaces of multipliers of Wiener amalgam spaces.