In this paper we are deal with the generalized translation operator generated by the Bessel operator in variable exponent Lebesgue spaces. The behavior of this generalized translation operator is well known on weighted Lebesgue spaces. But, there are some differences in the behavior of these operators on the variable exponent Lebesgue spaces. For example, the generalized translation operator is bounded in the variable exponent Lebesgue space \(L_{p(\cdot ),\gamma }(\mathbb{R}^{n}_{+})\) if and only if the exponent is constant. The aim of this paper is to give some the regularity conditions which ensure the boundedness of generalized translation operator \(T^{y} \) on variable exponent Lebesgue spaces if \(p\) is nonconstant.

在本文中，我们处理由Bessel算子在可变指数Lebesgue空间中生成的广义翻译算子。在加权Lebesgue空间上，此广义转换算子的行为是众所周知的。但是，这些运算符在可变指数Lebesgue空间上的行为存在一些差异。例如，广义翻译算子在变量指数Lebesgue空间\（L_ {p（\ cdot），\ gamma}（\ mathbb {R} ^ {n} _ {+}）\）中有界。指数是常数。本文的目的是给出一些规则性条件，如果\（p \）是非恒定的，则可以确保广义转换算子\（T ^ {y} \）在可变指数Lebesgue空间上的有界性。