Approximation by trigonometric polynomials and Faber-Laurent rational functions in grand Morrey spaces

Let G be finite Jordan domain bounded a Dini smoth curve Gamma in the complex plane C. We investigate the approximation properties of the partial sums of the Fourier series and prove direct theorem for approximation by polynomials in the subspace of Morrey spaces associated with grand Lebesgue spaces. Also, approximation properties of the Faber-Laurent rational series expansions in spaces Lp),lambda (Gamma) are studied. Direct theorems of approximation theory in grand Morrey-Smirnov classes, defined in domains with a Dini-smooth boundary, are proved.