TY - JOUR T1 - Some New Fourier and Jackson-Nikol'skii Type Inequalities In Unbounded Orthonormal Systems AU - Persson, Lars Erik AU - Akishev, Gabdolla AU - Singh, Harpal PY - 2021 DA - September DO - 10.33205/cma.910173 JF - Constructive Mathematical Analysis JO - CMA PB - Tuncer ACAR WT - DergiPark SN - 2651-2939 SP - 291 EP - 304 VL - 4 IS - 3 LA - en AB - We consider the generalized Lorentz space L ;q dened via a continuousand concave function and the Fourier series of a function with respect to an unboundedorthonormal system. Some new Fourier and Jackson-Nikol'skii type inequalities in this frameare stated, proved and discussed. In particular, the derived results generalize and unifyseveral well-known results but also some new applications are pointed out. KW - Inequalities KW - generalized Lorentz spaces KW - unbounded orthonormal system KW - Fourier inequalities KW - Jackson-Nikol'skii inequality CR - G. 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