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<p>In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem established following a density approach. To do this, a Luxemburg norm convergence theorem for the Steklov sampling series based on continuous functions with compact support, and a modular-type inequality in the case of functions in Orlicz spaces have been preliminary proved. As a particular case of general theory, the results in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>, in the Zygmund (interpolation), and in the exponential spaces are deduced. A crucial aspect in the above results is the choice of both band- and duration- limited kernel functions satisfying the partition of the unit property; to provide such examples an equivalent condition based on the Poisson summation formula and the computation of the Fourier transform of the kernel has been employed.</p>

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Modular convergence of Steklov sampling operators in Orlicz spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月6日

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  • Danilo Costarelli,
  • Erika Russo

摘要

In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem established following a density approach. To do this, a Luxemburg norm convergence theorem for the Steklov sampling series based on continuous functions with compact support, and a modular-type inequality in the case of functions in Orlicz spaces have been preliminary proved. As a particular case of general theory, the results in \(L^p\) L p , in the Zygmund (interpolation), and in the exponential spaces are deduced. A crucial aspect in the above results is the choice of both band- and duration- limited kernel functions satisfying the partition of the unit property; to provide such examples an equivalent condition based on the Poisson summation formula and the computation of the Fourier transform of the kernel has been employed.