Trigonometric approximation by Nörlund type means in -norm
Commentationes Mathematicae Universitatis Carolinae (2009)
- Volume: 50, Issue: 4, page 575-589
- ISSN: 0010-2628
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topSzal, Bogdan. "Trigonometric approximation by Nörlund type means in $L^p$-norm." Commentationes Mathematicae Universitatis Carolinae 50.4 (2009): 575-589. <http://eudml.org/doc/35132>.
@article{Szal2009,
abstract = {We show that the same degree of approximation as in the theorems proved by L. Leindler [Trigonometric approximation in $L^p$-norm, J. Math. Anal. Appl. 302 (2005), 129–136] and P. Chandra [Trigonometric approximation of functions in $L^p$-norm, J. Math. Anal. Appl. 275 (2002), 13–26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions.},
author = {Szal, Bogdan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {class $\operatorname\{Lip\} (\alpha ,p)$; $L^p$-norm; trigonometric approximation; class ; trigonometric approximation; -norm; Nörlund mean},
language = {eng},
number = {4},
pages = {575-589},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Trigonometric approximation by Nörlund type means in $L^p$-norm},
url = {http://eudml.org/doc/35132},
volume = {50},
year = {2009},
}
TY - JOUR
AU - Szal, Bogdan
TI - Trigonometric approximation by Nörlund type means in $L^p$-norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 4
SP - 575
EP - 589
AB - We show that the same degree of approximation as in the theorems proved by L. Leindler [Trigonometric approximation in $L^p$-norm, J. Math. Anal. Appl. 302 (2005), 129–136] and P. Chandra [Trigonometric approximation of functions in $L^p$-norm, J. Math. Anal. Appl. 275 (2002), 13–26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions.
LA - eng
KW - class $\operatorname{Lip} (\alpha ,p)$; $L^p$-norm; trigonometric approximation; class ; trigonometric approximation; -norm; Nörlund mean
UR - http://eudml.org/doc/35132
ER -
References
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- Chandra P., Functions of classes and and their Riesz means, Riv. Mat. Univ. Parma (4) 12 (1986), 275--282. Zbl0853.42002MR0913050
- Chandra P., A note on degree of approximation by Nörlund and Riesz operators, Mat. Vestnik 42 (1990), 9--10. Zbl0725.42004MR1096908
- Chandra P., 10.1016/S0022-247X(02)00211-1, J. Math. Anal. Appl. 275 (2002), 13--26. MR1941769DOI10.1016/S0022-247X(02)00211-1
- Leindler L., 10.1016/j.jmaa.2004.07.049, J. Math. Anal. Appl. 302 (2005), 129--136. MR2107350DOI10.1016/j.jmaa.2004.07.049
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- Quade E.S., 10.1215/S0012-7094-37-00342-9, Duke Math. J. 3 (1937), 529--542. Zbl0017.20501MR1546008DOI10.1215/S0012-7094-37-00342-9
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