Abstract:
We consider the convergence of Fourier series in the norm of Orlicz spaces
narrower than $L(e^x)$. It is shown that if a continuous function has
a non-summable derivative, then its Fourier series is not necessarily convergent
in the norm of these Orlicz spaces. We find a condition on a bounded function $f$
under which the Fourier series of $f$ is convergent in the norm of an
Orlicz space $L(\varphi)\subset L(e^x)$ and estimate the accuracy of this result.
Keywords:Fourier series, convergence, Lorentz spaces, local modulus of continuity.
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