Complex Interpolation of Modified Weighted Grand Lebesgue Spaces

In the present paper, we investigate the interpolation of weighted grand Lebesgue spaces by using the complex methods. We establish some inclusion results of complex interpolation between weighted grand Lebesgue spaces. In addition, we show that the first complex interpolation between modified weighted grand Lebesgue spaces coincides with the closure of essentially bounded functions with respect to the norm of the intermediate space. We also show that modified weighted grand Lebesgue spaces are closed under the second complex interpolation method. We also establish the complex interpolation results for (unweighted) grand Lebesgue spaces for distinct parameters τ, τ₁, and τ. Our results extend the complex interpolation of grand Lebesgue spaces in Hakim et al. (Monatsh Math 184:245–272, 2017).