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 $L^{p}$ spaces, $1\leq p < \infty$. We obtain new results on strong convergence of Fourier series for functions of generalized bounded variation. 
Muharem Avdispahi\'c and Zenan \v{S}abanac
math.CA