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

Gabdolla AKİSHEV, Lars Erik PERRSON, Harpal SİNGH
2021 Constructive Mathematical Analysis  
We consider the generalized Lorentz space L ψ,q defined via a continuous and concave function ψ 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.
doi:10.33205/cma.910173 fatcat:u6xduyqrxjdu3hvcw6o7spkamy