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August, 2022 On Sobolev-type Inequalities on Morrey Spaces of an Integral Form
Takao Ohno, Tetsu Shimomura
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Taiwanese J. Math. 26(4): 831-845 (August, 2022). DOI: 10.11650/tjm/220203

Abstract

We prove Sobolev-type inequalities for modified Riesz potentials of functions in Morrey spaces of an integral form over non-doubling metric measure spaces. Our results are new even for the doubling metric measure setting. In particular, our results extend the previous results in Morrey spaces of an integral form in the Euclidean case.

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Takao Ohno. Tetsu Shimomura. "On Sobolev-type Inequalities on Morrey Spaces of an Integral Form." Taiwanese J. Math. 26 (4) 831 - 845, August, 2022. https://doi.org/10.11650/tjm/220203

Information

Received: 8 August 2021; Revised: 7 February 2022; Accepted: 15 February 2022; Published: August, 2022
First available in Project Euclid: 23 February 2022

Digital Object Identifier: 10.11650/tjm/220203

Subjects:
Primary: 46E30
Secondary: 42B25

Keywords: maximal functions , metric measure space , Morrey spaces , Non-doubling measure , Riesz potential , Sobolev's inequality

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 4 • August, 2022
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