TY - GEN
T1 - Moduli of Smoothness and Rate of a.e. Convergence for Some Convolution Operators
AU - Stokolos, Alexander M.
AU - Trebels, Walter
PY - 2013
Y1 - 2013
N2 - 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 tμ, 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.
AB - 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 tμ, 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.
UR - http://www.scopus.com/inward/record.url?scp=84883424279&partnerID=8YFLogxK
U2 - 10.1007/978-1-4614-4565-4_27
DO - 10.1007/978-1-4614-4565-4_27
M3 - Conference article
SN - 9781461445647
T3 - Springer Proceedings in Mathematics and Statistics
SP - 339
EP - 355
BT - Recent Advances in Harmonic Analysis and Applications
PB - Springer New York LLC
ER -