Notes on the spaces of bilinear multipliers

Details Notes on the spaces of bilinear multipliers Notes on the spaces of bilinear multipliers

2009-05-26

arxiv.org/abs/0905.4151v1

Mathematics

Classical Analysis and ODEs

13 pages, Notes on the course given in La Falda (Argentina)2008

Scientific paper

A locally integrable function $m(\xi,\eta)$ defined on $\mathbb R^n\times \mathbb R^n$ is said to be a bilinear multiplier on $\mathbb R^n$ of type $(p_1,p_2, p_3)$ if $$ B_m(f,g)(x)=\int_{\mathbb R^n} \int_{\mathbb R^n}\hat f(\xi)\hat g(\eta)m(\xi,\eta)e^{2\pi i(<\xi +\eta,x>} d\xi d\eta$$ defines a bounded bilinear operator from $L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n) $ to $L^{p_3}(\mathbb R^n)$. The study of the basic properties of such spaces is investigated and several methods of constructing examples of bilinear multipliers are provided. The special case where $m(\xi,\eta)= M(\xi-\eta)$ for a given $M$ defined on $\mathbb R^n$ is also addressed.

Affiliated with

Also associated with

No associations

Rating

Notes on the spaces of bilinear multipliers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Notes on the spaces of bilinear multipliers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Notes on the spaces of bilinear multipliers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-646666