ANALISIS KETERBATASAN OPERATOR BESSEL-RIESZ DI RUANG LEBESGUE YANG TERDEFINISI PADA RUANG METRIK UKURAN

Awal Febriantono, NIM.: 20106010050 (2025) ANALISIS KETERBATASAN OPERATOR BESSEL-RIESZ DI RUANG LEBESGUE YANG TERDEFINISI PADA RUANG METRIK UKURAN. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

The limitations of the Bessel-Riesz operator have been extensively studied and developed by researchers, particularly in the field of mathematical analysis. This research examines the boundedness of the Bessel-Riesz operator in Lebesgue spaces defined on metric measure spaces. The Bessel-Riesz operator is a convolution of the Bessel-Riesz kernel and functions in Lebesgue spaces. Before proving the boundedness of the Bessel-Riesz operator, it is first shown that the Bessel-Riesz kernel satisfies the membership condition in the L1 space. Furthermore, the proof also utilizes the boundedness of the Hardy-Littlewood maximal operator in Lebesgue spaces. By leveraging the membership property of the Bessel-Riesz kernel in the L1 space and the boundedness of the Hardy-Littlewood maximal operator, the Bessel- Riesz operator is shown to be bounded from Lp to Lp.

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