Boundedness of some operators on variable exponent Fofana's spaces and their preduals

Let ۱ \leq p\leq \alpha \leq  q \leq \infty.  The  Fofana's spaces \left(L^{p},\ell^{q}\right)^{\alpha}(\mathbb{R}^d)  were introduced in ۱۹۸۸ by Fofana on the basis of Wiener amalgam spaces and their predual spaces \mathcal{H}(p',q',\alpha')(\mathbb{R}^d) have been described by Feichtinger and Feuto in ۲۰۱۹. Recently, in ۲۰۲۳, Yang and Zhou generalized these spaces by replacing the constant exponent p with the variable exponent  p(\cdot) and defining so the variable exponent Fofana's spaces \left(L^{p(\cdot)},\ell^{q}\right)^{\alpha}(\mathbb{R}^d) and their preduals \mathcal{H}(p'(\cdot),q',\alpha')(\mathbb{R}^d).  The purpose of this paper is to investigate the boundedness of classical operators such as Riesz potentials operators, maximal operators, Calderon-Zygmund operators and some generalized sublinear operators in both  \left(L^{p(\cdot)},\ell^{q}\right)^{\alpha}(\mathbb{R}^d) and \mathcal{H}(p'(\cdot),q',\alpha')(\mathbb{R}^d). In order to do this, we prove some properties of these spaces.  Our results extend and/or improve those of classical Fofana's spaces and their preduals.

کلیدواژه ها:

Fofana's spaces ، Variable exponent ، Riesz potentials operators ، Maximal operators ، Calderón-Zygmund operators ، Sublinear operators