Open Mathematics, vol.19, no.1, pp.306-315, 2021 (SCI-Expanded)
In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator (B-maximal operator) on Lp(middot;)γ(ℝnk,+) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the B-maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the B-maximal operator is not bounded on Lp(middot;)γ(ℝnk,+) variable exponent Lebesgue spaces in the case of p- = 1. We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional B-maximal function) on Lp(middot;)γ(ℝnk,+) variable exponent Lebesgue spaces.