Moduli of Smoothness and Rate of a.e. Convergence for Some Convolution Operators
Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov
One purpose of this chapter is to establish results on the rate of almost everywhere convergence of approximation processes of convolution type in Lp(Rn),where instead of a particular rate (like t μ, μ > 0, t → 0+), fractional moduli of smoothness are employed. An essential tool is a modified K-functional. Away from saturation orders these results are nearly optimal. A second purpose is to illustrate that the methods applied also work in other settings which feature a convolution/multiplier structure.
Stokolos, Alexander M., Walter Trebels.
"Moduli of Smoothness and Rate of a.e. Convergence for Some Convolution Operators."
Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov, Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander M. Stokolos, and Brett D. Wick (Ed.), 25: 339-355 New York, NY: Springer.
doi: 10.1007/978-1-4614-4565-4_27 isbn: 978-1-4614-4565-4