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On the convergence of Kantorovich operators in Morrey spaces
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Abstract
In this paper, we investigate Kantorovich operators on Morrey spaces. We first recall the main tool in the proof of the uniform boundedness of Kantorovich operators in Morrey spaces, namely a pointwise estimate of Kantorovich operators by the Hardy-Littlewood maximal operator. We also investigate the convergence of Kantorovich operators in Morrey spaces under weaker assumptions that is also true for the endpoint case. In addition, we obtain the rate of convergence of Kantorovich operators in Morrey spaces under the condition of Hölder continuity. Our result can be applicable to the function spaces in a recent result by Zeren, Ismailov and Karacam.
MSC (2020): 41A10, 41A25, 42B35, 47B38
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Title: On the convergence of Kantorovich operators in Morrey spaces
Description:
Abstract
In this paper, we investigate Kantorovich operators on Morrey spaces.
We first recall the main tool in the proof of the uniform boundedness of Kantorovich operators in Morrey spaces, namely a pointwise estimate of Kantorovich operators by the Hardy-Littlewood maximal operator.
We also investigate the convergence of Kantorovich operators in Morrey spaces under weaker assumptions that is also true for the endpoint case.
In addition, we obtain the rate of convergence of Kantorovich operators in Morrey spaces under the condition of Hölder continuity.
Our result can be applicable to the function spaces in a recent result by Zeren, Ismailov and Karacam.
MSC (2020): 41A10, 41A25, 42B35, 47B38.
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