Mathematics – Analysis of PDEs
Scientific paper
2009-07-29
Mathematics
Analysis of PDEs
Scientific paper
In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and strong inequalities for the multilinear fractional integral operator. In particular, we extend some results given in \cite{CPSS} to the multilinear context. On the other hand we prove weighted pointwise estimates between the multilinear fractional maximal operator ${\cal M}_{\alpha,B}$ associated to a Young function $B$ and the multilinear maximal operators ${\cal M}_{\psi}={\cal M}_{0,\psi}$, $\psi(t)=B(t^{1-\alpha/(nm)})^{{nm}/{(nm-\alpha)}}$. As an application of these estimate we obtain a direct proof of the $L^p-L^q$ boundedness results of ${\cal M}_{\alpha,B}$ for the case $B(t)=t$ and $B_k(t)=t(1+\log^+t)^k$ when $1/q=1/p-\alpha/n$. We also give sufficient conditions on the weights involved in the boundedness results of ${\cal M}_{\alpha,B}$ that generalizes those given in \cite{M} for $B(t)=t$. Finally, we prove some boundedness results in Banach function spaces for a generalized version of the multilinear fractional maximal operator.
No associations
LandOfFree
Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators 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 Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-468339