We revisit the properties of Bessel-Riesz operators and refine the proof of
the boundedness of these operators on generalized Morrey spaces using Young's
inequality. We also obtain an estimate for the norm of these operators on
generalized Morrey spaces. In addition, we reprove the boundedness of
fractional integral operators on generalized Morrey spaces and estimate their
norm.Comment: 10 page

Eridani

Gunawan, Hendra

Idris, Mochammad

English

arXiv

summary: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

Eridani, A.

Czech digital mathematics library

Norm estimates for Bessel-Riesz operators on generalized Morrey spaces

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

Mochammad Idris

Hendra Gunawan

Universitas Airlangga Repository

Institute of Mathematics AS CR, v. v. i.

https://repository.unair.ac.id/98532/2/C05_%28Fulltext%29_4%20%28Q3%20%3D%200.25%29%20%283%29%20mb-004517%20%28t%29.pdf

Norm estimates for Bessel-Riesz operators on generalized Morrey spaces

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Czech digital mathematics library

Universitas Airlangga Repository

Institute of Mathematics AS CR, v. v. i.