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

Yongrui Tang; Shujuan Zhou

doi:10.4134/JKMS.j230246

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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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

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

Yongrui Tang, Shujuan Zhou

Qingdao University; Qingdao University

Abstract

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Abstract

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).