Commutators with Reisz Potentials in One and Several Parameters
| dc.creator | Lacey, Michael T | |
| dc.date | 2005-02-16 | |
| dc.date | 2006-01-18 | |
| dc.date.accessioned | 2026-07-07T06:39:27Z | |
| dc.date.available | 2026-07-07T06:39:27Z | |
| dc.description | Let $ M_b$ be the operator of pointwise multiplication by $b$, that is $\operatorname M_b f=bf$. Set $[ A,B]={} AB- BA$. The Reisz potentials are the operators $$ R_αf(x)=\int f(x-y)\frac{dy}{\abs y ^α},\qquad 0<α<1. $$ They map $L^p\mapsto L^q$, for $1-α+\frac1q=\frac1p$, a fact we shall take for granted in this paper. A Theorem of Chanillo \cite{MR84j:42027} states that one has the equivalence $$ \norm [ M_b, R_α].p\to q.\simeq \norm b.\operatorname{BMO}. $$ with the later norm being that of the space of functions of bounded mean oscillation. We discuss a new proof of this result in a discrete setting, and extend part of the equivalence above to the higher parameter setting. | |
| dc.description | To appear in Hokkaido Math J. This is the final version of the paper. Several typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0502336 | |
| dc.identifier | http://arxiv.org/abs/math/0502336 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101081 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Commutators with Reisz Potentials in One and Several Parameters | |
| dc.type | text |