Mathematica Bohemica, Vol. 143, No. 4, pp. 409-417, 2018


Norm estimates for Bessel-Riesz operators on generalized Morrey spaces

Mochammad Idris, Hendra Gunawan, Eridani

Received May 11, 2017.   First published March 7, 2018.

Abstract:  We revisit the properties of Bessel-Riesz operators and present a different proof of the boundedness of these operators on generalized Morrey spaces. We also obtain an estimate for the norm of these operators on generalized Morrey spaces in terms of the norm of their kernels on an associated Morrey space. As a consequence of our results, we reprove the boundedness of fractional integral operators on generalized Morrey spaces, especially of exponent $1$, and obtain a new estimate for their norm.
Keywords:  Bessel-Riesz operator; fractional integral operator; generalized Morrey space
Classification MSC:  42B20, 26A33, 42B25, 26D10
DOI:  10.21136/MB.2018.0045-17


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Affiliations:   Mochammad Idris, Department of Mathematics, Institute of Technology Bandung, Bandung 40132, Indonesia, e-mail: idemath@gmail.com ( permanent address: Department of Mathematics, Lambung Mangkurat University, Banjarbaru Campus, Banjarbaru 70714, Indonesia); Hendra Gunawan, Department of Mathematics, Institute of Technology Bandung, Bandung 40132, Indonesia, e-mail: hgunawan@math.itb.ac.id; Eridani, Department of Mathematics, Airlangga University, Campus C Mulyorejo, Surabaya 60115, Indonesia, e-mail: eridani.dinadewi@gmail.com


 
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