More on Contributions of Non-Separable Spaces to Solving the Evolution Equation: The Case of Weighted Generalized Morrey Spaces

Abstract The study of some signal processing problems within Bayesian frameworks and semigroups theory, in the case where the Banach space under consideration may be nonseparable, was discussed in the paper published in 2022 by two of the authors. For the Cauchy problem for the diffusion equation, which is a typical example of evolution equation, there was studied the question of what can be saved in the study of the problem in the case with the initial data in the nonseparable classical Morrey space. In this paper we develop this approach to an essentially more general case of generalized Morrey spaces with general weights. The study is based on emersion of such spaces into weighted Lebesgue spaces with Muckenhoupt weights.