APPROXIMATION BY TRIGONOMETRIC POLYNOMIALS AND FABER-LAURENT RATIONAL FUNCTIONS IN GRAND MORREY SPACES
Abstract
Let G be nite Jordan domain bounded a Dini smoth curve ???? in
the complex plane C: We investigate the approximation properties of the par-
tial 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); (????) are studied. Direct theorems of approxima-
tion theory in grand Morrey-Smirnov classes, dened in domains with a Dini-
smooth boundary, are proved.:
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