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J. Korean Math. Soc. 2024; 61(2): 341-356

Online first article February 19, 2024      Printed March 1, 2024

https://doi.org/10.4134/JKMS.j230246

Copyright © The Korean Mathematical Society.

A note on Sobolev type trace inequalities for $s$-harmonic extensions

Yongrui Tang, Shujuan Zhou

Qingdao University; Qingdao University

Abstract

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In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.

Keywords: Sobolev trace inequalities, Besov spaces, fractional Poisson kernels, Hardy inequalities

MSC numbers: Primary 26D10, 46E35, 30H25

Supported by: This research was partly supported by National Natural Science Foundation of China (No. 12071272) and Shandong Natural Science Foundation of China (No. ZR2020MA004).

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