Some New Fourier and Jackson-Nikol'skii Type Inequalities In Unbounded Orthonormal Systems

Year 2021, Volume: 4 Issue: 3, 291 - 304, 16.09.2021

Gabdolla Akishev , Lars Erik Persson , Harpal Singh

https://doi.org/10.33205/cma.910173

Abstract

We consider the generalized Lorentz space L ;q dened via a continuous
and concave function and the Fourier series of a function with respect to an unbounded
orthonormal system. Some new Fourier and Jackson-Nikol'skii type inequalities in this frame
are stated, proved and discussed. In particular, the derived results generalize and unify
several well-known results but also some new applications are pointed out.

Keywords

Inequalities, generalized Lorentz spaces, unbounded orthonormal system, Fourier inequalities, Jackson-Nikol'skii inequality

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