Open Access
2016 Integral Restriction for Bilinear Operators
Weiren Zhao, Meng Wang, Guoping Zhao
Publ. Mat. 60(2): 485-500 (2016). DOI: 10.5565/PUBLMAT_60216_06


We consider the integral domain restriction operator $T_{\Omega}$ for certain bilinear operator $T$. We obtain that if $(s,p_1,p_2)$ satisfies $\frac{1}{p_1}+\frac{1}{p_2}\geq \frac{2}{\min\{1,s\}}$ and $\|T\|_{L^{p_1}\times L^{p_2}\rightarrow L^s}\lt\infty$, then $\|T_{\Omega}\|_{L^{p_1}\times L^{p_2}\rightarrow L^s}\lt\infty$. For some special domain $\Omega$, this property holds for triplets $(s,p_1,p_2)$ satisfying $\frac{1}{p_1}+\frac{1}{p_2}\gt\frac{1}{\min\{1,s\}}$.


Download Citation

Weiren Zhao. Meng Wang. Guoping Zhao. "Integral Restriction for Bilinear Operators." Publ. Mat. 60 (2) 485 - 500, 2016.


Received: 3 November 2014; Revised: 21 January 2016; Published: 2016
First available in Project Euclid: 11 July 2016

zbMATH: 1345.42028
MathSciNet: MR3521497
Digital Object Identifier: 10.5565/PUBLMAT_60216_06

Primary: 42B25

Keywords: Integral restriction , ‎multilinear operator‎

Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.60 • No. 2 • 2016
Back to Top