On Multidimensional Ideal Convergence via Matrix Summability Techniques

The primary objective of this paper is to provide a comprehensive characterization of the multiplier space associated with the summability fields generated by four-dimensional RH-regular matrices. In order to achieve this goal, we take into account the framework of $\mathfrak{A}$-statistically convergent double sequences and develop $\mathfrak{B}$-summability techniques formulated via ideals. This approach not only extends the classical theory of summability but also creates a broader setting where convergence phenomena can be investigated in greater generality. Furthermore, we explore and establish several fundamental properties of these newly introduced summability methods, with particular emphasis on their structural behavior, inclusion relations, and regularity conditions. Through these investigations, the study aims to contribute both to the theoretical understanding of multiplier spaces and to the potential applications of summability theory in analysis and related fields.