Translator Disclaimer
February 2018 Certain bilinear operators on Morrey spaces
Dashan FAN, Fayou ZHAO
Hokkaido Math. J. 47(1): 143-159 (February 2018). DOI: 10.14492/hokmj/1520928063

Abstract

In this paper, we consider that $T(f,g)$ is a bilinear operator satisfying \begin{equation*} |T(f,g)(x)|\preceq \int_{\mathbb{R}^{n}}\frac{|f(x-ty)g(x-y)|}{|y|^{n}}dy \end{equation*} for $x$ such that $0\notin {\rm supp}~(f(x-t\cdot )) \cap {\rm supp}~(g(x+\cdot ))$. We obtain the boundedness of $T(f,g)$ on the Morrey spaces with the assumption of the boundedness of the operator $T(f,g)$ on the Lebesgues spaces. As applications, we yield that many well known bilinear operators, as well as the first Calderón commutator, are bounded from the Morrey spaces $L^{q,\lambda_{1}}\times L^{r,\lambda_{2}}$ to $L^{p,\lambda}$, where $\lambda /p={\lambda_{1}}/{q}+{\lambda_{2}}/{r}$.

Citation

Download Citation

Dashan FAN. Fayou ZHAO. "Certain bilinear operators on Morrey spaces." Hokkaido Math. J. 47 (1) 143 - 159, February 2018. https://doi.org/10.14492/hokmj/1520928063

Information

Published: February 2018
First available in Project Euclid: 13 March 2018

zbMATH: 06853594
MathSciNet: MR3773728
Digital Object Identifier: 10.14492/hokmj/1520928063

Subjects:
Primary: 42B20, 42B25, 42B35

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 1 • February 2018
Back to Top