On moduli of smoothness and approximation by trigonometric polynomials in weighted Lorentz spaces

Year 2016, Volume: 45 Issue: 6, 1675 - 1684, 01.12.2016

Sadulla Z. Jafarov

Abstract

We investigate the approximation properties of the functions by
trigonometric polynomials in weighted Lorentz spaces with weights satisfying so called Muckenhoupt's Ap condition. Relations between moduli of smoothness of the derivatives of the functions and those of the
functions itself are studied. In weighted Lorentz spaces we also prove a
theorem on the relationship between the derivatives of a polynomial of
best approximation and the best approximation of the function. Moreover, we study relationship between modulus of smoothness of the function and its de la Vallée-Poussin sums in these spaces.

Keywords

moduli of smoothness, weighted Lorentz spaces, Muckenhoupt weight, trigonometric approximation, best approximation

References

• . . .