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19. 12. 2016.
Strong boundedness, strong convergence and generalized variation
A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all $${L^{p}}$$Lp spaces, $${1\leq p < \infty}$$1≤p<∞. We obtain new results on strong convergence of Fourier series for functions of generalized bounded variation.