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

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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