We show that several definitions of algebras of continuous Fourier multipliers on variable Lebesgue spaces over the real line are equivalent under some natural assumptions on variable exponents. Some of our results are new even in the case of standard Lebesgue spaces and give answers on two questions about algebras of continuous Fourier multipliers on Lebesgue spaces over the real line posed by Mascarenhas, Santos and Seidel.

中文翻译：

---

可变Lebesgue空间上连续Fourier乘子的代数。

我们表明，在可变指数的某些自然假设下，实线上可变Lebesgue空间上连续傅立叶乘法器的代数的几种定义是等效的。即使在标准Lebesgue空间的情况下，我们的一些结果也是新的，并且给出了关于在Mascarenhas，Santos和Seidel所构成的实线上Lebesgue空间上的连续Fourier乘子的代数的两个问题的答案。