In this paper I provide more general notions for generalized Fourier series and convergence of Fourier series in Lorentz-Morrey space with many groups of variables. This conceptual ramework is very important in other areas in mathematics (such as ordinary and partial differential equations) and physics (such as quantum mechanics and electrodynamics). As applications I study of summability of Fourier coefficients for functions from some Lorentz-Morrey type spaces with many groups of variables.
In this paper I provide more general notions for generalized Fourier series and convergence of Fourier series in Lorentz-Morrey space with many groups of variables. This conceptual framework is very important in other areas in mathematics (such as ordinary and partial differential equations) and physics (such as quantum mechanics and electrodynamics). As applications I study of summability of Fourier coefficients for functions from some Lorentz-Morrey type spaces with many groups of variables.