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Let {Hn(t)} be a sequence of non-negative, even, and continuous functions on ℝ. In this paper, we consider a convolution operator Jn(f;x)=∫0∞f(t)Hn(t−x)dt, f∈Lp(R+), and then investigate the local saturation of Jn(f;x).

Local saturation of a positive linear convolution operator