Approximation by Haar polynomials in variable exponent grand Lebesgue spaces

Abstract

In this paper, we give direct theorems on approximation by Haar and Walsh polynomials in variable exponent grand Lebesgue space. Also the degree of approximation by Borel, Abel-Poisson, Riesz-Zygmund and Euler linear means of Haar-Fourier series are treated in the above-cited space.

Keywords:

• Haar system
• variable exponent grand Lebesgue space
• direct approximation theorem
• linear means of Haar–Fourier series

Mathematics Subject Classification (2010):

• 42C10
• 46E30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of author is supported by Program of Development of Regional Scientific and Educational Mathematical Center ‘Mathematics of Future Technologies’ (grant no. 075-02-2023-949).