Abstract
Let $$L^p_w[-1,1]$$ be the weighted Lebesgue space on $$[-1,1]$$ with $$w(t)=(1-t^2)^{-1/2}$$. We prove that the rate of convergence in $$L^p_w[-1,1]$$ of the Fejer sums is equivalent to a fractional modulus of smoothness of order 1/2.
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