Mean Convergence of Entire Interpolations in Weighted Space

Abstract We investigate the convergence of entire Lagrange interpolations and Hermite exponential type $$\tau $$ τ , as \rightarrow \infty xmlns:mml="http://www.w3.org/1998/Math/MathML">τ→∞ in weighted $$L^p$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Lp -spaces on real line. The weights are reciprocals functions that depend may be viewed smoothed versions a target weight w . statements obtained from Marcinkiewicz inequalities for functions. apply our main results to deal with power weights.