In this paper, we establish a quantitative estimate for Durrmeyer-sampling type operators in the general framework of Orlicz spaces, using a suitable modulus of smoothness defined by the involved modular functional. As a consequence of the above result, we can deduce quantitative estimates in several instances of Orlicz spaces, such as L pspaces, Zygmund spaces and the exponential spaces. By using a direct approach, we also provide a further estimate in the particular case of L p-spaces, with 1 ≤ p < +∞, that turns out to be sharper than the previous general one. Moreover, we deduce the qualitative order of convergence, when functions belonging to suitable Lipschitz classes are considered.

Quantitative estimates for Durrmeyer-sampling series in Orlicz spaces / Costarelli, Danilo; Piconi, Michele; Vinti, Gianluca. - In: SAMPLING THEORY, SIGNAL PROCESSING, AND DATA ANALYSIS. - ISSN 2730-5716. - ELETTRONICO. - 21:(2022), pp. 3.0-3.0. [10.1007/s43670-022-00042-6]

Quantitative estimates for Durrmeyer-sampling series in Orlicz spaces

Piconi, Michele;
2022

Abstract

In this paper, we establish a quantitative estimate for Durrmeyer-sampling type operators in the general framework of Orlicz spaces, using a suitable modulus of smoothness defined by the involved modular functional. As a consequence of the above result, we can deduce quantitative estimates in several instances of Orlicz spaces, such as L pspaces, Zygmund spaces and the exponential spaces. By using a direct approach, we also provide a further estimate in the particular case of L p-spaces, with 1 ≤ p < +∞, that turns out to be sharper than the previous general one. Moreover, we deduce the qualitative order of convergence, when functions belonging to suitable Lipschitz classes are considered.
2022
21
0
0
Costarelli, Danilo; Piconi, Michele; Vinti, Gianluca
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1291395
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