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<p>In this article, we study the approximation behavior of the linear integral operators in the settings of Morrey spaces. Under some assumptions on the kernel function, first we obtain the pointwise and uniform approximation for bounded continuous and bounded uniformly continuous functions, respectively. Next we get error estimates for these operators in terms of a <i>K</i>-functional. We study the regularization properties of these operators. Furthermore, using the equivalence of the <i>K</i>-functional and the modulus of smoothness in the Morrey space setting, we obtain a characterization of the generalized Lipschitz classes in terms of convergence of the linear integral operators. Towards the end, we provide some examples of specific kernels which satisfy the required assumptions.</p>

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On approximation by linear integral operators in the settings of Morrey spaces

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Nitin Bartwal,
  • A. Sathish Kumar

摘要

In this article, we study the approximation behavior of the linear integral operators in the settings of Morrey spaces. Under some assumptions on the kernel function, first we obtain the pointwise and uniform approximation for bounded continuous and bounded uniformly continuous functions, respectively. Next we get error estimates for these operators in terms of a K-functional. We study the regularization properties of these operators. Furthermore, using the equivalence of the K-functional and the modulus of smoothness in the Morrey space setting, we obtain a characterization of the generalized Lipschitz classes in terms of convergence of the linear integral operators. Towards the end, we provide some examples of specific kernels which satisfy the required assumptions.